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Volume 46 (2), July-December 2022

  • Abstract: In this work we study the problem of modelling and forecasting the dynamics of the influenza virus in Brazil at a given month, from data on reported cases and genetic diversity collected from previous months, in other locations. Granger causality is employed as a tool to assess possible predictive relationships between covariates. For modelling and forecasting purposes, a time series regression approach is applied considering lagged information regarding reported cases and genetic diversity in other regions. Three different models are analysed, including stepwise time series regression and LASSO.

    Keywords: Flu, time series regression, variable selection, genetic diversity, Granger causality

    Pages: 161–188


  • Abstract: The Split-Then-Combine approach has previously been used to generate the weights of forecasts in a combination in the Euclidean space. This paper extends this approach to combine forecasts inside the simplex space, the sample space of positive weights adding up to one. As it turns out, the simplicial statistic given by the sample centre compares favourably against the fixed-weight, average forecast. Besides, we also develop a Combination-After-Selection method to get rid of redundant forecasters. We apply these approaches to make out-of-sample one-step ahead combinations and subcombinations of forecasts for several economic variables. This methodology is particularly useful when the sample size is smaller than the number of forecasts, a case where other methods (e.g., ordinary least squares or principal component analysis) are not applicable.

    Keywords: Aitchison geometry, Combination-After-Selection, Dimensionality problem, Simplex, Split-Then-Combine

    Pages: 189–216


  • Abstract: This paper recasts the problem of missing values in the covariates of a regression model as a latent Gaussian Markov random field (GMRF) model in a fully Bayesian framework. The proposed approach is based on the definition of the covariate imputation sub-model as a latent effect with a GMRF structure. This formulation works for continuous covariates but for categorical covariates a typical multiple imputation approach is employed. Both techniques can be easily combined for the case in which continuous and categorical variables have missing values. The resulting Bayesian hierarchical model naturally fts within the integrated nested Laplace approximation (INLA) framework, which is used for model fitting. Hence, this work fills an important gap in the INLA methodology as it allows to treat models with missing values in the covariates. As in any other fully Bayesian framework, by relying on INLA for model fitting it is possible to formulate a joint model for the data, the imputed covariates and their missingness mechanism. In this way, it is possible to tackle the more general problem of assessing the missingness mechanism by conducting a sensitivity analysis on the different alternatives to model the non-observed covariates. Finally, the proposed approach is illustrated in two examples on modeling health risk factors and disease mapping.

    Keywords: Imputation, missing values, GMRF, INLA, sensitivity analysis

    Pages: 217–244


  • Abstract: To generate a circular distribution, we use the alternate-wrapping technique (unlike the usual wrapping), by wrapping in the alternate directions, after each single-wrapping. The resulting distribution is called alternate-wrapped distribution. Some general properties and distinctions between the two wrapping schemes are indicated. As an illustration, alternate-wrapped-exponential distribution and alternate-wrapped-normal distribution are considered. The moment and maximum likelihood estimator of the parameters of alternative-wrapped-exponential distribution are obtained and their performance is evaluated using simulation. Maximum likelihood estimators are obtained for the parameters of the alternate-wrapped-normal distribution and simulation study is conducted, and this distribution is used to analyse a real-life data set and is compared with the wrapped normal distribution.

    Keywords: Akaike information criterion, Bayesian information criterion, circular distribution, exponential distribution, trigonometric moments, wrapped normal distribution

    Pages: 245–262


Volume 46 (1), January-June 2022

  • Abstract: The Hawkes process is a self-exciting Poisson point process, characterised by a conditional intensity function. Since its introduction fifty years ago, it has been the subject of numerous research directions and continues to inspire new methodological and theoretical developments as well as new applications. This paper marks half a century of interest in Hawkes processes by presenting a snapshot of four state-of-the-art research directions, categorised as frequentist and Bayesian methods, other modelling approaches and notable theoretical developments. A particular focus is on nonparametric approaches, with advances in kernel estimation and computational efficiencies. A survey of real world applications is provided to illustrate the breadth of application of this remarkable approach.

    Keywords: Hawkes process, point process, nonparametric

    Pages: 3–38


  • Abstract: At least one unusual event appears in some count datasets. It will lead to a more concentrated (or dispersed) distribution than the Poisson, gamma, Weibull, Conway-Maxwell-Poisson (CMP), and Faddy (1997) models can accommodate. These well-known count models are based on the monotonic rates of interarrival times between successive events. Under the assumption of non-monotonic rates and independent exponential interarrival times, a new class of parametric models for unusual-event (UE) count data is proposed. These models are applied to two empirical applications, the number of births and the number of bids, and yield considerably better results to the above well-known count models.

    Keywords: Poisson count model, Gamma count model, Weibull count model, Conway-Maxwell-Poisson count model, Faddy count model

    Pages: 39–66


  • Abstract: In this paper, we consider the problem of estimating the finite population cumulative distribution function (CDF) in a complex survey sampling, which includes two-stage and three-stage cluster sampling schemes with and without stratification. We propose two new families of CDF estimators using supplementary information on a single auxiliary variable. Explicit mathematical expressions of the biases and mean squared errors of the proposed CDF estimators are developed under the first order of the approximation. Real datasets are also considered to support the proposed theory.

    Keywords: Ratio estimator, exponential ratio estimator, auxiliary information, stratification, two-stage and three-stage cluster sampling, relative efficiencies, bias, mean-squared error

    Pages: 67–94


  • Abstract: In this article we consider an extension of the penalized splines approach in the context of censored semiparametric modelling using Kaplan-Meier weights to take into account the effect of censorship. We proposed an estimation method and develop statistical inferences in the model. Using various simulation studies we show that the performance of the method is quite satisfactory. A real data set is used to illustrate that the proposed method is comparable to parametric approaches when assuming a probability distribution of the response variable and/or the functional form. However, our proposal does not need these assumptions since it avoids model specification problems

    Keywords: Censored data, Kaplan-Meier weights, P-splines, semiparametric models, survival analysis

    Pages: 95– 114


  • Abstract: Precision medicine allows the extraction of information from complex datasets to facilitate clinical decision-making at the individual level. Topological Data Analysis (TDA) offers promising tools that complement current analytical methods in precision medicine studies. We introduce the fundamental concepts of the TDA corpus (the simplicial complex, the Mapper graph, the persistence diagram and persistence landscape). We show how these can be used to enhance the prediction of clinical outcomes and to identify novel subpopulations of interest, particularly applied to understand remission of depression in data from the GENDEP clinical trial.

    Keywords: Precision medicine, data shape, topology, topological data analysis, persistence diagram, Mapper, persistence landscapes, machine learning

    Pages: 115– 136


  • Abstract: In the context of logistic regression models, a cut-off point is usually selected to dichotomize the estimated predicted probabilities based on the model. The techniques proposed to estimate optimal cut-off points in the literature, are commonly developed to be applied in simple random samples and their applicability to complex sampling designs could be limited. Therefore, in this work we propose a methodology to incorporate sampling weights in the estimation process of the optimal cut-off points, and we evaluate its performance using a real data-based simulation study. The results suggest the convenience of considering sampling weights for estimating optimal cut-off points.

    Keywords: Optimal cut-off points, complex survey data, sampling weights

    Pages: 137– 158


Volume 45 (2), July-December 2021

  • Abstract: In this paper, a general nonparametric estimator of the probability of default is proposed and studied. It is derived from an estimator of the conditional survival function for censored data obtained with a double smoothing, on the covariate and on the variable of interest. An empirical study, based on modified real data, illustrates its practical application and a simulation study shows the performance of the proposed estimator and compares its behaviour with smoothed estimators only in the covariate. Asymptotic expressions for the bias and the variance of the probability of default estimator are found and asymptotic normality is proved.

    Keywords: Censored data, kernel method, probability of default, risk analysis, survival analysis

    Pages: 93–120


  • Abstract: Due to the large amount of accidents negatively affecting the wellbeing of the survivors and their families, a substantial amount of research is conducted to determine the causes of road accidents. This type of data come in the form of non-negative integers and may be modelled using the Poisson regression model. Unfortunately, the commonly used maximum likelihood estimator is unstable when the explanatory variables of the Poisson regression model are highly correlated. Therefore, this paper proposes a new almost unbiased estimator which reduces the instability of the maximum likelihood estimator and at the same time produce smaller mean squared error. We study the statistical properties of the proposed estimator and a simulation study has been conducted to compare the performance of the estimators in the smaller mean squared error sense. Finally, Swedish traffic fatality data are analyzed to show the benefit of the proposed method.

    Keywords: Applied traffic modeling, Maximum likelihood estimator, mean squared error matrix, Poisson regression, simulation study, traffic fatality

    Pages: 121–142


  • Abstract: Laparoscopy is an operation carried out in the abdomen through small incisions with visual control by a camera. This technique needs the abdomen to be insufflated with carbon dioxide to obtain a working space for surgical instruments’ manipulation. Identifying the critical point at which insufflation should be limited is crucial to maximizing surgical working space and minimizing injurious effects. A Bayesian nonlinear growth mixed-effects model for the relationship between the insufflation pressure and the intra–abdominal volume generated is discussed as well as its plausibility to represent the data.

    Keywords: Intra-abdominal pressure, logistic growth function, Markov chain, Monte Carlo methods, random effects

    Pages: 143–162


  • Abstract: Bilinear regression models involving a nonlinear interaction term are applied in many fields (e.g., Goodman’s RC model, Lee-Carter mortality model or CAPM financial model). In many of these contexts data often exhibit extreme values. We propose the use of bilinear models to estimate the median of the conditional distribution in the presence of extreme values. The aim of this paper is to provide alternative methods to estimate median bilinear models. A calibration strategy based on an iterative estimation process of a sequence of median linear regression is developed. Mean and median bilinear models are compared in two applications with extreme observations. The first application deals with simulated data. The second application refers to Spanish mortality data involving years with atypical high mortality (Spanish flu, civil war and HIV/AIDS). The performance of the median bilinear model was superior to that of the mean bilinear model. Median bilinear models may be a good alternative to mean bilinear models in the presence of extreme values when the centre of the conditional distribution is of interest.

    Keywords: Outliers, quantile regression, single factor models, nonlinear, multiplicative

    Pages: 163–180


  • Abstract: In this paper we introduce an extension of the power Maxwell distribution. We also discuss a reparametrized version of this model applied to quantile regression. Some properties of the model and estimation based on the maximum likelihood estimation method are studied. We also present a simulation study to assess the performance of estimators in such finite samples, and two applications to real data sets to illustrate the model. .

    Keywords: Maxwell distribution, exponentiated distributions, maximum likelihood, quantile regression

    Pages: 181–200


Volume 45 (1), January-June 2021

  • Abstract: This article is a tribute to the contributions of Florence Nightingale to statistics and statistical graphics on her bicentennial. We start with her most famous “rose” diagram and describe how she came to this graphic, designed to influence medical practice in the British army. But this study takes us backward in time to consider where and when the ideas of radial diagrams arose, why they were useful, and why we call these her “radiant diagrams.”

    Keywords: Data visualization, polar area diagram, radial diagram, nursing, sanitation

    Pages: 3–18

    DOI: 10.2436/20.8080.02.106

  • Abstract: We construct credible intervals to estimate the mean organism (zooplankton and phytoplankton) concentration in ballast water via a decision-theoretic approach. To obtain the required optimal sample size, we use a total cost minimization criterion defined as the sum of the sampling cost and the Bayes risk either under a Poisson or a negative binomial model for organism counts, both with a gamma prior distribution. Such credible intervals may be employed to verify whether the ballast water discharged from a ship is in compliance with international standards. We also conduct a simulation study to evaluate the credible interval lengths associated with the proposed optimal sample sizes.

    Keywords: Optimal sample size, Bayes risk, Poisson distribution, negative binomial distribution

    Pages: 19–32

    DOI: 10.2436/20.8080.02.107

  • Abstract: Dating is a key element for archaeologists. We propose a Bayesian approach to provide chronology to sites that have neither radiocarbon dating nor clear stratigraphy and whose only information comes from lithic arrowheads. This classifier is based on the Dirichlet-multinomial inferential process and posterior predictive distributions. The procedure is applied to predict the period of a set of undated sites located in the east of the Iberian Peninsula during the 4th and 3rd millennium cal BC.

    Keywords: Bifacial flint arrowheads, chronological model, Dirichlet-multinomial process, posterior predictive distribution, radiocarbon dating

    Pages: 33–46

    DOI: 10.2436/20.8080.02.108

  • Abstract: In regression, the quality of estimators is known to be very sensitive to the presence of spurious variables and outliers. Unfortunately, this is a frequent situation when dealing with real data. To handle outlier proneness and achieve variable selection, we propose a robust method performing the outright rejection of discordant observations together with the selection of relevant variables. A natural way to define the corresponding optimization problem is to use the ℓ0 norm and recast it as a mixed integer optimization problem. To retrieve this global solution more efficiently, we suggest the use of additional constraints as well as a clever initialization. To this end, an efficient and scalable non-convex proximal alternate algorithm is introduced. An empirical comparison between the ℓ0 norm approach and its ℓ1 relaxation is presented as well. Results on both synthetic and real data sets provided that the mixed integer programming approach and its discrete first order warm start provide high quality solutions.

    Keywords: Robust optimization, statistical learning, linear regression, variable selection, outlier detection, mixed integer programming

    Pages: 47–66


  • Abstract: This paper proposes a generalized framework to analyze spatial count data under a unilateral regular lattice structure based on thinning type models. We start from the simple spatial integer-valued auto-regressive model of order 1. We extend this model in certain directions. First, we consider various distributions as choices for the innovation distribution to allow for additional overdispersion. Second, we allow for use of covariate information, leading to a non-stationary model. Finally, we derive and use other models related to this simple one by considering simplification on the existing model. Inference is based on conditional maximum likelihood approach. We provide simulation results under different scenarios to understand the behaviour of the conditional maximum likelihood. A real data application is also provided. Remarks on how the results extend to other families of models are also given.

    Keywords: Unilateral, spatial, regular, lattice, thinning

    Pages: 67–90

    DOI: 10.2436/20.8080.02.110

Volume 44 (2), July-December 2020

  • Abstract: In order to apply group sequential methods for interim analysis for early stopping in clinical trials, the joint distribution of test statistics over time has to be known. Often the distribution is multivariate normal or asymptotically so, and an application of group sequential methods requires multivariate integration to determine the group sequential boundaries. However, if the increments between successive test statistics are independent, the multivariate integration reduces to a univariate integration involving simple recursion based on convolution. This allows application of standard group sequential methods. In this paper we review group sequential methods and the development that established independent increments in test statistics for the primary outcomes of longitudinal or failure time data.

    Keywords: Failure time data, interim analysis, longitudinal data, clinical trials, repeated significance tests, sequential methods

    Pages: 223–264

    DOI: 10.2436/20.8080.02.101

  • Abstract: A new discrete two-parameter distribution is introduced by discretizing a generalized half-normal distribution. The model is useful for fitting overdispersed as well as underdispersed data. The failure function can be decreasing, bathtub shaped or increasing. A reparameterization of the distribution is introduced for use in a regression model based on the median. The behaviour of the maximum likelihood estimates is studied numerically, showing good performance in finite samples. Three real data set applications reveal that the new model can provide a better explanation than some other competitors.

    Keywords: Discretizing, generalized half-normal distribution, failure function, health, quantile regression, stochastic order

    Pages: 265–284

    DOI: 10.2436/20.8080.02.102

  • Abstract: A major operational task in city logistics is related to waste collection. Due to large problem sizes and numerous constraints, the optimization of real-life waste collection problems on a daily basis requires the use of metaheuristic solving frameworks to generate near-optimal collection routes in low computation times. This paper presents a simheuristic algorithm for the time-dependent waste collection problem with stochastic travel times. By combining Monte Carlo simulation with a biased randomized iterated local search metaheuristic, time-varying and stochastic travel speeds between different network nodes are accounted for. The algorithm is tested using real instances in a medium-sized city in Spain.

    Keywords: Waste collection management, vehicle routing problem, stochastic optimization, simheuristics, biased randomization, case study

    Pages: 285–310

    DOI: 10.2436/20.8080.02.103

  • Abstract: Many decision-making processes in our society involve NP-hard optimization problems. The largescale, dynamism, and uncertainty of these problems constrain the potential use of stand-alone optimization methods. The same applies for isolated simulation models, which do not have the potential to find optimal solutions in a combinatorial environment. This paper discusses the utilization of modelling and solving approaches based on the integration of simulation with metaheuristics. These ‘simheuristic’ algorithms, which constitute a natural extension of both metaheuristics and simulation techniques, should be used as a ‘first-resort’ method when addressing large-scale and NP-hard optimization problems under uncertainty –which is a frequent case in real-life applications. We outline the benefits and limitations of simheuristic algorithms, provide numerical experiments that validate our arguments, review some recent publications, and outline the best practices to consider during their design and implementation stages.

    Keywords: Simulation, metaheuristics, combinatorial optimization, simheuristics

    Pages: 311–334

    DOI: 10.2436/20.8080.02.104

  • Abstract: Mixed Poisson models are most relevant to the analysis of longitudinal count data in various disciplines. A conventional specification of such models relies on the normality of unobserved heterogeneity effects. In practice, such an assumption may be invalid, and non-normal cases are appealing. In this paper, we propose a modelling strategy by allowing the vector of effects to follow the multivariate skew-normal distribution. It can produce dependence between the correlated longitudinal counts by imposing several structures of mixing priors. In a Bayesian setting, the estimation process proceeds by sampling variants from the posterior distributions. We highlight the usefulness of our approach by conducting a simulation study and analysing two real-life data sets taken from the German Socioeconomic Panel and the US Centers for Disease Control and Prevention. By a comparative study, we indicate that the new approach can produce more reliable results compared to traditional mixed models to fit correlated count data.

    Keywords: Bayesian computation, correlated random effects, hierarchical representation, longitudinal data, multivariate skew-normal distribution, over-dispersion

    Pages: 335–356

    DOI: 10.2436/20.8080.02.105

Volume 44 (1), January-June 2020

  • Abstract: Average incomes and poverty proportions are additive parameters obtained as averages of a given function of an income variable. As the variable income has an asymmetric distribution, it is not properly modelled via normal distributions. When dealing with this type of variable, a first option is to apply transformations that approximate normality. A second option is to use nonsymmetric distributions from the exponential family. This paper proposes unit-level generalized linear mixed models for modelling asymmetric positive variables and for deriving three types of predictors of small area additive parameters, called empirical best, marginal and plug-in. The parameters of the introduced model are estimated by applying the maximum likelihood method to the Laplace approximation of the likelihood. The mean squared errors of the predictors are estimated by parametric bootstrap. The introduced methodology is applied and illustrated under unit-level gamma mixed models. Some simulation experiments are carried out to study the behaviour of the fitting algorithm, the small area predictors and the bootstrap estimator of the mean squared errors. By using data of the Spanish living condition survey of 2013, an application to the estimation of average incomes and poverty proportions in counties of the region of Valencia is given.

    Keywords: Average income, poverty proportion, generalized linear mixed models, empirical best predictor, mean squared error, bootstrap

    Pages: 3–38

    DOI: 10.2436/20.8080.02.93

  • Abstract: Archetypal analysis is an exploratory tool that explains a set of observations as mixtures of pure (extreme) patterns. If the patterns are actual observations of the sample, we refer to them as archetypoids. For the first time, we propose to use archetypoid analysis for binary observations. This tool can contribute to the understanding of a binary data set, as in the multivariate case. We illustrate the advantages of the proposed methodology in a simulation study and two applications, one exploring objects (rows) and the other exploring items (columns). One is related to determining student skill set profiles and the other to describing item response functions.

    Keywords: Dichotomous item test, archetypal analysis, functional data analysis, item response theory, skill profile

    Pages: 39–66

    DOI: 10.2436/20.8080.02.94

  • Abstract: One of the main challenges researchers face is to identify the most relevant features in a prediction model. As a consequence, many regularized methods seeking sparsity have flourished. Although sparse, their solutions may not be interpretable in the presence of spurious coefficients and correlated features. In this paper we aim to enhance interpretability in linear regression in presence of multicollinearity by: (i) forcing the sign of the estimated coefficients to be consistent with the sign of the correlations between predictors, and (ii) avoiding spurious coefficients so that only significant features are represented in the model. This will be addressed by modelling constraints and adding them to an optimization problem expressing some estimation procedure such as ordinary least squares or the lasso. The so-obtained constrained regression models will become Mixed Integer Quadratic Problems. The numerical experiments carried out on real and simulated datasets show that tightening the search space of some standard linear regression models by adding the constraints modelling (i) and/or (ii) help to improve the sparsity and interpretability of the solutions with competitive predictive quality.

    Keywords: Linear regression, Multicollinearity, Sparsity, Cardinality constraint, Mixed Integer Non Linear Programming

    Pages: 67–98

    DOI: 10.2436/20.8080.02.95

  • Abstract: The logratio-normal-multinomial distribution is a count data model resulting from compounding a multinomial distribution for the counts with a multivariate logratio-normal distribution for the multinomial event probabilities. However, the logratio-normal-multinomial probability mass function does not admit a closed form expression and, consequently, numerical approximation is required for parameter estimation. In this work, different estimation approaches are introduced and evaluated. We concluded that estimation based on a quasi-Monte Carlo Expectation-Maximisation algorithm provides the best overall results. Building on this, the performances of the Dirichlet-multinomial and logratio-normal-multinomial models are compared through a number of examples using simulated and real count data.

    Keywords: Count data, Compound probability distribution, Dirichlet Multinomial, Logratio coordinates, Monte Carlo method, Simplex

    Pages: 99–126

    DOI: 10.2436/20.8080.02.96

  • Abstract: In this paper, we obtain the Bartlett factor for the likelihood ratio statistic and the Bartlett-type correction factor for the score and gradient test in censored data from a Weibull distribution. The expressions derived are simple, we only have to define a few matrices. We conduct an extensive Monte Carlo study to evaluate the performance of the corrected tests in small sample sizes and we show how they improve the original versions. Finally, we apply the results to a real data set with a small sample size illustrating that conclusions about the regressors could be different if corrections were not applied to the three mentioned classical statistics for the hypothesis test.

    Keywords: Bartlett correction, censored data, Weibull distribution, chi-squared distribution, maximum likelihood estimates, type I and II censoring

    Pages: 127–140

    DOI: 10.2436/20.8080.02.97

  • Abstract: The introduction of Electric Vehicles (EVs) in modern fleets facilitates green road transportation. However, the driving ranges of EVs are limited by the duration of their batteries, which arise new operational challenges. Hybrid fleets of gas and EVs might be heterogeneous both in loading capacities as well as in driving-range capabilities,whichmakes the design of efficient routing plans a difficult task. In this paper, we propose a newMulti-Round IteratedGreedy (MRIG) metaheuristic to solve the Heterogeneous Vehicle Routing Problem with Multiple Driving ranges and loading capacities (HeVRPMD). MRIG uses a successive approximations method to offer the decision maker a set of alternative fleet configurations,with different distance-based costs and green levels. The numerical experiments show that MRIG is able to outperform previous works dealing with the homogeneous version of the problem, which assumes the same loading capacity for all vehicles in the fleet. The numerical experiments also confirm that the proposed MRIG approach extends previous works by solving a more realistic HeVRPMD and provides the decision-maker with fleets with higher green levels.

    Keywords: Vehicle Routing Problem, Electric Vehicles, Heterogeneous Fleet, Multiple Driving Ranges. Iterated Greedy heuristic, Successive Approximations Method

    Pages: 141–170

    DOI: 10.2436/20.8080.02.98

  • Abstract: An important problem in Statistics is the study of longitudinal data taking into account the effect of other explanatory variables, such as treatments and time and, simultaneously, the incorporation into the model of the time dependence between observations on the same individual. The latter is specially relevant in the case of nonstationary correlations, and nonconstant variances for the different time point at which measurements are taken. Antedependence models constitute a well known commonly used set of models that can accommodate this behaviour. These covariance models can include too many parameters and estimation can be a complicated optimization problem requiring the use of complex algorithms and programming. In this paper, a new Bayesian approach to analyse longitudinal data within the context of antedependence models is proposed. This innovative approach takes into account the possibility of having nonstationary correlations and variances, and proposes a robust and computationally efficient estimation method for this type of data. We consider the joint modelling of the mean and covariance structures for the general antedependence model, estimating their parameters in a longitudinal data context. Our Bayesian approach is based on a generalization of the Gibbs sampling and Metropolis-Hastings by blocks algorithm, properly adapted to the antedependence models longitudinal data settings. Finally, we illustrate the proposed methodology by analysing several examples where antedependence models have been shown to be useful: the small mice, the speech recognition and the race data sets.

    Keywords: Antedependence models, Bayesian methods, Gibbs sampling, Mean-covariance modelling, Nonstationary correlation

    Pages: 171–200

    DOI: 10.2436/20.8080.02.99

  • Abstract: Compositional data analysis is concerned with the relative importance of positive variables, expressed through their log-ratios. The literature has proposed a range of manners to compute log-ratios, some of whose interrelationships have never been reported when used as explanatory variables in regression models. This article shows their similarities and differences in interpretation based on the notion that one log-ratio has to be interpreted keeping all others constant. The article shows that centred, additive, pivot, balance and pairwise log-ratios lead to simple reparametrizations of the same model which can be combined to provide useful tests and comparable effect size estimates.

    Keywords: Compositional regression models, CoDa, composition as explanatory, centred log-ratios, pivot coordinates, pairwise log-ratios, additive log-ratios, effect size

    Pages: 201–220

    DOI: 10.2436/20.8080.02.100

Volume 43 (2), July-December 2019

  • Abstract: The inclusion of stakeholder behaviour in Operations Research / Industrial Engineering (OR/IE) models has gained much attention in recent years. Behavioural and cognitive traits of people and groups have been integrated in simulation models (mainly through agent-based approaches) as well as in optimization algorithms. However, especially the influence of relations between different actors in human networks is a broad and interdisciplinary topic that has not yet been fully investigated. This paper analyses, from an OR/IE point of view, the existing literature on behaviour-related factors in human networks. This review covers different application fields, including: supply chain management, public policies in emergency situations, and Internet-based human networks. The review reveals that the methodological approach of choice (either simulation or optimization) is highly dependent on the application area. However, an integrated approach combining simulation and optimization is rarely used. Thus, the paper proposes the hybridization of simulation with optimization as one of the best strategies to incorporate human behaviour in human networks and the resulting uncertainty, randomness, and dynamism in related OR/IE models.

    Keywords: Modelling human behaviour, human networks, simulation, optimization, simheuristics

    Pages: 193–222

    DOI: 10.2436/20.8080.02.85

  • Abstract: We propose a new type of risk measure for non-negative random variables that focuses on the tail of the distribution. The measure is inspired in general parametric distributions that are well-known in the statistical analysis of the size of income. We derive simple expressions for the conditional moments of these distributions, and we show that they are suitable for analysis of tail risk. The proposed method can easily be implemented in practice because it provides a simple one-step way to compute value-at-risk and tail value-at-risk. We show an illustration with currency exchange data. The data and implementation are open access for reproducibility.

    Keywords: Moments, multi-period risk assessment, value-at-risk

    Pages: 223–236

    DOI: 10.2436/20.8080.02.86

  • Abstract: False discovery rate (FDR) control is important in multiple testing scenarios that are common in neuroimaging experiments, and p-values from such experiments may often arise from some discretely supported distribution or may be grouped in some way. Two situations that may lead to discretely supported distributions are when the p-values arise from Monte Carlo or permutation tests are used. Grouped p-values may occur when p-values are quantized for storage. In the neuroimaging context, grouped p-values may occur when data are stored in an integer-encoded form. We present a method for FDR control that is applicable in cases where only p-values are available for inference, and when those p-values are discretely supported or grouped. We assess our method via a comprehensive set of simulation scenarios and find that our method can outperform commonly used FDR control schemes in various cases. An implementation to a mouse imaging data set is used as an example to demonstrate the applicability of our approach.

    Keywords: Censored data, data quantization, discrete support, empirical-Bayes, false discovery rate control, grouped data, incompletely observed data, mixture model

    Pages: 237–258

    DOI: 10.2436/20.8080.02.87

  • Abstract: Interval-grouped data appear when the observations are not obtained in continuous time, but monitored in periodical time instants. In this framework, a nonparametric kernel distribution estimator is proposed and studied. The asymptotic bias, variance and mean integrated squared error of the new approach are derived. From the asymptotic mean integrated squared error, a plug-in bandwidth is proposed. Additionally, a bootstrap selector to be used in this context is designed. Through a comprehensive simulation study, the behaviour of the estimator and the bandwidth selectors considering different scenarios of data grouping is shown. The performance of the different approaches is also illustrated with a real grouped emergence data set of Avena sterilis (wild oat).

    Keywords: Bootstrap bandwidth, cumulative distribution function estimator, interval data, plug-in bandwidth

    Pages: 259–288

    DOI: 10.2436/20.8080.02.88

  • Abstract: It is well known that outliers can affect both the estimation of parameters and volatilities when fitting a univariate GARCH-type model. Similar biases and impacts are expected to be found on correlation dynamics in the context of multivariate time series. We study the impact of outliers on the estimation of correlations when fitting multivariate GARCH models and propose a general detection algorithm based on wavelets, that can be applied to a large class of multivariate volatility models. Its effectiveness is evaluated through a Monte Carlo study before it is applied to real data. The method is both effective and reliable, since it detects very few false outliers.

    Keywords: Correlations, multivariate GARCH models, outliers, wavelets.

    Pages: 289–316

    DOI: 10.2436/20.8080.02.89

  • Abstract: We propose a class of goodness–of–fit test procedures for arbitrary parametric families of circular distributions with unknown parameters. The tests make use of the specific form of the characteristic function of the family being tested, and are shown to be consistent. We derive the asymptotic null distribution and suggest that the new method be implemented using a bootstrap resampling technique that approximates this distribution consistently. As an illustration, we then specialize this method to testing whether a given data set is from the von Mises distribution, a model that is commonly used and for which considerable theory has been developed. An extensive Monte Carlo study is carried out to compare the new tests with other existing omnibus tests for this model. An application involving five real data sets is provided in order to illustrate the new procedure.

    Keywords: Goodness-of-fit, Circular data, Empirical characteristic function, Maximum likelihood estimation, von Mises distribution.

    Pages: 317–336

    DOI: 10.2436/20.8080.02.90

  • Abstract: Public services, such as higher education, medical services, libraries or public administration offices, provide services to their customers. To obtain opinion-satisfaction indices of customers, it would be necessary to survey all the customers of the service (census), which is impossible. What is possible is to estimate the indices by surveying a random customer sample. The efficiency obtained with the classic data envelopment analysis models, considering the opinion indices of the customers of the public service as output data estimated with a user sample, will be an estimation of the obtained efficiency if the census is available. This paper proposes a bootstrap methodology to build a confidence region to simultaneously estimate the population data envelopment analysis efficiency score vector of a set of public service-producing units, with a fixed confidence level and using deterministic input data and estimated customer opinion indices as output data. The usefulness of the result is illustrated by describing a case study comparing the efficiency of libraries.

    Keywords: Data envelopment analysis, sampling survey research, public sector, bootstrap, simultaneous confidence region.

    Pages: 337–354

    DOI: 10.2436/20.8080.02.91

  • Abstract: In this article, we consider two univariate random environment integer-valued autoregressive processes driven by the same hidden process. A model of this kind is capable of describing two correlated non-stationary counting time series using its marginal variable parameter values. The properties of the model are presented. Some parameter estimators are described and implemented on the simulated time series. The introduction of this bivariate integer-valued autoregressive model with a random environment is justified at the end of the paper, where its real-life data-fitting performance was checked and compared to some other appropriate models. The forecasting properties of the model are tested on a few data sets, and forecasting errors are discussed through the residual analysis of the components that comprise the model.

    Keywords: INAR, negative binomial thinning, random states, time series of count, non-stationary process.

    Pages: 355–384

    DOI: 10.2436/20.8080.02.92

Volume 43 (1), January-June 2019

  • Abstract: Green transportation is becoming relevant in the context of smart cities, where the use of electric vehicles represents a promising strategy to support sustainability policies. However the use of electric vehicles shows some drawbacks as well, such as their limited driving-range capacity. This paper analyses a realistic vehicle routing problem in which both driving-range constraints and stochastic travel times are considered. Thus, the main goal is to minimize the expected time-based cost required to complete the freight distribution plan. In order to design reliable Routing plans, a simheuristic algorithm is proposed. It combines Monte Carlo simulation with a multi-start metaheuristic, which also employs biased-randomization techniques. By including simulation, simheuristics extend the capabilities of metaheuristics to deal with stochastic problems. A series of computational experiments are performed to test our solving approach as well as to analyse the effect of uncertainty on the routing plans.

    Keywords: Vehicle routing problem, electric vehicles, green transport and logistics, smart cities, simheuristics, biased-randomized heuristics

    Pages: 3–24

    DOI: 10.2436/20.8080.02.77

  • Abstract: We introduce new consistent and scale-free goodness-of-fit tests for the exponential distribution based on the Puri-Rubin characterization. For the construction of test statistics we employ weighted L2 distance between V-empirical Laplace transforms of random variables that appear in the characterization. We derive the asymptotic behaviour under the null hypothesis as well as under fixed alternatives. We compare our tests, in terms of the Bahadur efficiency, to the likelihood ratio test, as well as some recent characterization based goodness-of-fit tests for the exponential distribution. We also compare the power of our tests to the power of some recent and classical exponentiality tests. According to both criteria, our tests are shown to be strong and outperform most of their competitors.

    Keywords: Goodness-of-fit, exponential distribution, Laplace transform, Bahadur efficiency, V-statistics with estimated parameters

    Pages: 25–50

    DOI: 10.2436/20.8080.02.78

  • Abstract: In this paper we propose a Bayesian hierarchical spatio-temporal model for the joint analysis of multiple diseases which includes specific and shared spatial and temporal effects. Dependence on shared terms is controlled by disease-specific weights so that their posterior distribution can be used to identify diseases with similar spatial and temporal patterns. The model proposed here has been used to study three different causes of death (oral cavity, esophagus and stomach cancer) in Spain at the province level. Shared and specific spatial and temporal effects have been estimated and mapped in order to study similarities and differences among these causes. Furthermore, estimates using Markov chain Monte Carlo and the integrated nested Laplace approximation are compared.

    Keywords: Bayesian modelling, Joint modelling, Multivariate disease mapping, Shared components. Spatio-temporal epidemiology

    Pages: 51–74

    DOI: 10.2436/20.8080.02.79

  • Abstract: Road freight transportation includes various internal and external costs that need to be accounted for in the construction of efficient routing plans. Typically, the resulting optimization problem is formulated as a vehicle routing problem in any of its variants. While the traditional focus of the vehicle routing problem was the minimization of internal routing costs such as travel distance or duration, numerous approaches to include external factors related to environmental routing aspects have been recently discussed in the literature. However, internal and external routing costs are often treated as competing objectives. This paper discusses the internalization of external routing costs through the consideration of green taxes and green tolls. Numeric experiments with a biased-randomization savings algorithm, show benefits of combining internal and external costs in delivery route planning.

    Keywords: Vehicle routing problem, biased randomization, green logistics, negative road externalities, internalization

    Pages: 75–94

    DOI: 10.2436/20.8080.02.80

  • Abstract: In the last decades, a lot of research papers applying statistical methods for analysing sports data have been published. Football, also called soccer, is one of the most popular sports all over the world organised in national championships in a round robin format in which the team reaching the most points at the end of the tournament wins the competition. The aim of this work is to develop a suitable probability model for studying the points achieved by a team in a football match. For this purpose, we built a discrete probability distribution taking values, zero for losing, one for a draw and three for a victory. We test its performance using data from the Spanish Football League (First division) during the 2013-14 season. Furthermore, the model provides an attractive framework for predicting points and incorporating covariates in order to study the factors affecting the points achieved by the teams.

    Keywords: Covariate, football data, forecasting, regression, sport statistics, truncated distribution, weighted distribution

    Pages: 95–112

    DOI: 10.2436/20.8080.02.81

  • Abstract: Pearson’s chi-square test is widely employed in social and health sciences to analyse categorical data and contingency tables. For the test to be valid, the sample size must be large enough to provide a minimum number of expected elements per category. This paper develops functions for regrouping strata automatically, thus enabling the goodness-of-fit test to be performed within an iterative procedure. The usefulness and performance of these functions is illustrated by means of a simulation study and the application to different datasets. Finally, the iterative use of the functions is applied to the Continuous Sample of Working Lives, a dataset that has been used in a considerable number of studies, especially on labour economics and the Spanish public pension system.

    Keywords: Goodness-of-fit chi-square test, statistical software, Visual Basic for Applications, Mathematica, Continuous Sample of Working Lives

    Pages: 113–142

    DOI: 10.2436/20.8080.02.83

  • Abstract: When the same data are used to fit a model and estimate its predictive performance, this estimate may be optimistic, and its correction is required. The aim of this work is to compare the behaviour of different methods proposed in the literature when correcting for the optimism of the estimated area under the receiver operating characteristic curve in logistic regression models. A simulation study (where the theoretical model is known) is conducted considering different number of covariates, sample size, prevalence and correlation among covariates. The results suggest the use of k-fold cross-validation with replication and bootstrap.

    Keywords: Prediction models, logistic regression, area under the receiver operating characteristic curve, validation, bootstrap

    Pages: 145–162

    DOI: 10.2436/20.8080.02.82

  • Abstract: The problem of finding optimal exact designs is more challenging than that of approximate optimal designs. In the present paper, we develop two efficient algorithms to numerically construct exact designs for mixture experiments. The first is a novel approach to the well-known multiplicative algorithm based on sets of permutation points, while the second uses genetic algorithms. Using (i) linear and non-linear models, (ii) D- and I-optimality criteria, and (iii) constraints on the ingredients, both approaches are explored through several practical problems arising in the chemical, pharmaceutical and oil industry.

    Keywords: Optimal experimental design, D-optimality, I-optimality, mixture experiments, multiplicative algorithm, genetic algorithm, exact designs

    Pages: 163–190

    DOI: 10.2436/20.8080.02.84

Volume 42 (2), July-December 2018

  • Abstract: The discrete case of Bayes’ formula is considered the paradigm of information acquisition. Prior and posterior probability functions, as well as likelihood functions, called evidence functions, are compositions following the Aitchison geometry of the simplex, and have thus vector character. Bayes’ formula becomes a vector addition. The Aitchison norm of an evidence function is introduced as a scalar measurement of information. A fictitious fire scenario serves as illustration. Two different inspections of affected houses are considered. Two questions are addressed: (a) which is the information provided by the outcomes of inspections, and (b) which is the most informative inspection.

    Keywords: Evidence function, Bayes’ formula, Aitchison geometry, compositions, orthonormal basis, simplex, scalar information

    Pages: 101–124

    DOI: 10.2436/20.8080.02.71

  • Abstract: Nearest neighbour methods are employed for drawing inferences about spatial patterns of points from two or more classes. We introduce a new pattern called correspondence which is motivated by (spatial) niche/habitat specificity and segregation, and define an associated contingency table called a correspondence contingency table, and examine the relation of correspondence with the motivating patterns (namely, segregation and niche specificity). We propose tests based on the correspondence contingency table for testing self and mixed correspondence and determine the appropriate null hypotheses and the underlying conditions appropriate for these tests. We compare finite sample performance of the tests in terms of empirical size and power by extensive Monte Carlo simulations and illustrate the methods on two artificial data sets and one real-life ecological data set.

    Keywords: Association, complete spatial randomness, habitat/niche specificity, independence, random labelling, segregation

    Pages: 125–158

    DOI: 10.2436/20.8080.02.72

  • Abstract: One of the main sources of inaccuracy in modern survey techniques, such as online and smartphone surveys, is the absence of an adequate sampling frame that could provide a probabilistic sampling. This kind of data collection leads to the presence of high amounts of bias in final estimates of the survey, specially if the estimated variables (also known as target variables) have some influence on the decision of the respondent to participate in the survey. Various correction techniques, such as calibration and propensity score adjustment or PSA, can be applied to remove the bias. This study attempts to analyse the efficiency of correction techniques in multiple situations, applying a combination of propensity score adjustment and calibration on both types of variables (correlated and not correlated with the missing data mechanism) and testing the use of a reference survey to get the population totals for calibration variables. The study was performed using a simulation of a fictitious population of potential voters and a real volunteer survey aimed to a population for which a complete census was available. Results showed that PSA combined with calibration results in a bias removal considerably larger when compared with calibration with no prior adjustment. Results also showed that using population totals from the estimates of a reference survey instead of the available population data does not make a difference in estimates accuracy, although it can contribute to slightly increment the variance of the estimator.

    Keywords: Online surveys, Smartphone surveys, propensity score adjustment, calibration, simulation

    Pages: 159–182

    DOI: 10.2436/20.8080.02.73

  • Abstract: Surveys applying quota sampling in their final step are widely used in opinion and market research all over the world. This is also the case in Spain, where the surveys carried out by CIS (a public institution for sociological research supported by the government) have become a point of reference. The rules used by CIS to select individuals within quotas, however, could be improved as they lead to biases in age distributions. Analysing more than 545,000 responses collected in the 220 monthly barometers conducted between 1997 and 2016 by CIS, we compare the empirical distributions of the barometers with the expected distributions from the sample design and/or target populations. Among other results, we find, as a consequence of the rules used, significant overrepresentations in the observed proportions of respondents with ages equal to the minimum and maximum of each quota (age and gender group). Furthermore, in line with previous literature, we also note a significant overrepresentation of ages ending in zero. After offering simple solutions to avoid all these biases, we discuss some of their consequences for modelling and inference and about limitations and potentialities of CIS data

    Keywords: Centre for Sociological Research, quota sampling, fieldwork rules, age and gender groups, inter-quota distributions, intra-quota distributions

    Pages: 183–206

    DOI: 10.2436/20.8080.02.74

  • Abstract: Authentication of extra virgin olive oil requires fast and cost-effective analytical procedures, such as near infrared spectroscopy. Multivariate analysis and chemometrics have been successfully applied in several papers to gather qualitative and quantitative information of extra virgin olive oils from near infrared spectra. Moreover, there are many examples in the literature analysing the effect of agro-climatic conditions on food content, in general, and in olive oil components, in particular. But the majority of these studies considered a factor, a non-numerical variable, containing this meteorological information. The present work uses all the agro-climatic data with the aim of highlighting the linear relationships between them and the near infrared spectra. The study begins with a graphical motivation, continues with a bivariate analysis and, finally, applies redundancy analysis to extend and confirm the previous conclusions.

    Keywords: Extra virgin olive oil, infrared spectroscopy, agro-climatic data, linear correlations, redundancy analysis

    Pages: 209–236

    DOI: 10.2436/20.8080.02.75

  • Abstract: Two new implementations for fitting Poisson excess relative risk methods are proposed for assumed simple models. This allows for estimation of the excess relative risk associated with a unique exposure, where the background risk is modelled by a unique categorical variable, for example gender or attained age levels. Additionally, it is shown how to fit general Poisson linear relative risk models in R. Both simple methods and the R fitting are illustrated in three examples. The first two examples are from the radiation epidemiology literature. Data in the third example are randomly generated with the purpose of sharing it jointly with the R scripts.

    Keywords: Radiation epidemiology, Poisson non-linear regression, improper priors, R programming

    Pages: 237–252

    DOI: 10.2436/20.8080.02.76

Volume 42 (1), January-June 2018

  • Abstract: In this paper, it is proposed a Bayesian analysis of a time series in the presence of a random change-point and autoregressive terms. The development of this model was motivated by a data set related to the monthly number of asthma medications dispensed by the public health services of Ribeirão Preto, Southeast Brazil, from 1999 to 2011. A pronounced increase trend has been observed from 1999 to a specific change-point, with a posterior decrease until the end of the series. In order to obtain estimates for the parameters of interest, a Bayesian Markov Chain Monte Carlo (MCMC) simulation procedure using the Gibbs sampler algorithm was developed. The Bayesian model with autoregressive terms of order 1 fits well to the data, allowing to estimate the change-point at July 2007, and probably reflecting the results of the new health policies and previously adopted programs directed toward patients with asthma. The results imply that the present model is useful to analyse the monthly number of dispensed asthma medications and it can be used to describe a broad range of epidemiological time series data where a change-point is present.

    Keywords: Time series, regression models, Bayesian methods, change-point model, epidemiological data

    Pages: 3–26

    DOI: 10.2436/20.8080.02.66

  • Abstract: In this paper we study the complexity of a functional data set drawn from particular processes by means of a two-step approach. The first step considers a new graphical tool for assessing to which family the data belong: the main aim is to detect whether a sample comes from a monomial or an exponential family. This first tool is based on a nonparametric kNN estimation of small ball probability. Once the family is specified, the second step consists in evaluating the extent of complexity by estimating some specific indexes related to the assigned family. It turns out that the developed methodology is fully free from assumptions on model, distribution as well as dominating measure. Computational issues are carried out by means of simulations and finally the method is applied to analyse some financial real curves dataset.

    Keywords: Small ball probability, log-Volugram, random processes, complexity class, complexity index, knn estimation, functional data analysis

    Pages: 27–44

    DOI: 10.2436/20.8080.02.67

  • Abstract: Suppose the regression vector-parameter is subjected to lie in a subspace hypothesis in a linear regression model. In situations where the use of least absolute and shrinkage selection operator (LASSO) is desired, we propose a restricted LASSO estimator. To improve its performance, LASSO-type shrinkage estimators are also developed and their asymptotic performance is studied. For numerical analysis, we used relative efficiency and mean prediction error to compare the estimators which resulted in the shrinkage estimators to have better performance compared to the LASSO.

    Keywords: Double shrinking, LASSO, preliminary test LASSO, restricted LASSO, Stein-type shrinkage LASSO

    Pages: 45–58

    DOI: 10.2436/20.8080.02.68

  • Abstract: Heteroscedasticity produces a lack of type I error control in Student’s t test for difference between means. Pretesting for it (e.g., by means of Levene’s test) should be avoided as this also induces type I error. These pretests are inadequate for their objective: not rejecting the null hypotheses is not a proof of homoscedasticity; and rejecting it may simply suggest an irrelevant heteroscedasticity. We propose a method to establish irrelevance limits for the ratio of variances. In conjunction with a test for dispersion equivalence, this appears to be a more affordable pretesting strategy.

    Keywords: Homoscedasticity, equivalence test, indifference zone, pretest, Student’s t test

    Pages: 59–72

    DOI: 10.2436/20.8080.02.69

  • Abstract: Usual assumptions on the statistical properties of daily net cash flows include normality, absence of correlation and stationarity. We provide a comprehensive study based on a real-world cash flow data set showing that: (i) the usual assumption of normality, absence of correlation and stationarity hardly appear; (ii) non-linearity is often relevant for forecasting; and (iii) typical data transformations have little impact on linearity and normality. This evidence may lead to consider a more data-driven approach such as time-series forecasting in an attempt to provide cash managers with expert systems in cash management.

    Keywords: Statistics, forecasting, cash flow, non-linearity, time-series

    Pages: 73–98

    DOI: 10.2436/20.8080.02.70

Volume 41 (2), July-December 2017

  • Abstract: Molenberghs, Verbeke, and Demétrio (2007) and Molenberghs et al. (2010) proposed a general framework to model hierarchical data subject to within-unit correlation and/or overdispersion. The framework extends classical overdispersion models as well as generalized linear mixed models. Subsequent work has examined various aspects that lead to the formulation of several extensions. A unified treatment of the model framework and key extensions is provided. Particular extensions discussed are: explicit calculation of correlation and other moment-based functions, joint modelling of several hierarchical sequences, versions with direct marginally interpretable parameters, zero-inflation in the count case, and influence diagnostics. The basic models and several extensions are illustrated using a set of key examples, one per data type (count, binary, multinomial, ordinal, and time-to-event).

    Keywords: Conjugacy, frailty, joint modelling, marginalized multilevel model, mixed model, overdispersion, underdispersion, variance component, zero-inflation.

    Pages: 191–254

    DOI: 10.2436/20.8080.02.58

  • Abstract: We study the factors which may affect students’ marks in two modules, mathematics and statistics, taught consecutively in the first year of a Business Administration Studies degree course. For this purpose, we introduce a suitable bivariate regression model in which the dependent variables have bounded support and the marginal means are functions of explanatory variables. The marginal probability density functions have a classical beta distribution. Simulation experiments were performed to observe the behaviour of the maximum likelihood estimators. Comparisons with univariate beta regression models show the proposed bivariate regression model to be superior.

    Keywords: Beta distribution, bivariate beta distribution, conditional distributions, covariate, marginal distributions, regression, mathematics, statistics, business studies.

    Pages: 255–276

    DOI: 10.2436/20.8080.02.59

  • Abstract: A methodological approach for modelling the spatial distribution of bioclimatic indices is proposed in this paper. The value of the bioclimatic index is modelled with a hierarchical Bayesian model that incorporates both structured and unstructured random effects. Selection of prior distributions is also discussed in order to better incorporate any possible prior knowledge about the parameters that could refer to the particular characteristics of bioclimatic indices. MCMC methods and distributed programming are used to obtain an approximation of the posterior distribution of the parameters and also the posterior predictive distribution of the indices. One main outcome of the proposal is the spatial bioclimatic probability distribution of each bioclimatic index, which allows researchers to obtain the probability of each location belonging to different bioclimates. The methodology is evaluated on two indices in the Island of Cyprus.

    Keywords: Bioclimatology, geostatistics, parallel computation, spatial prediction.

    Pages: 277–296

    DOI: 10.2436/20.8080.02.60

  • Abstract: Cutaneous melanoma is thought to be triggered by intense, occasional exposure to ultraviolet radiation, either from the sun or tanning beds, especially in people who are genetically predisposed to the disease. When skin cells are damaged by ultraviolet light in this way, often showing up as a sunburn, they are more prone to genetic defects that cause them to rapidly multiply and form potentially fatal (malignant) tumors. Melanoma originates in a type of skin cell called a melanocyte, such cells help produce the pigments of our skin, hair, and eyes. We propose a new cure rate survival regression model for predicting cutaneous melanoma. We assume that the unknown number of competing causes that can influence the survival time is governed by a power series Distribution and that the time until the tumor cells are activated follows the Pareto IV distribution. The parameter estimation is based on the EM algorithm which for this model can be implemented in a simple way in computational terms. Simulation studies are presented, showing the good performance of the proposed estimation procedure. Finally, two real applications related to a cutaneous melanoma and melanoma data sets are presented.

    Keywords: Competing risks, cure rate models, EM algorithm, Pareto IV distribution, power series distribution.

    Pages: 297–318

    DOI: 10.2436/20.8080.02.61

  • Abstract: This paper has two complementary objectives: on the one hand, it introduces the EURO method for the estimation of (regional) Social Accounting Matrices. This method is widely used by Eurostat for the estimation of missing national Supply, Use and Input-output tables but it has not been used before within the context of social accounting matrices or of regional statistics and/or regional impact analyses. On the other hand, this work discusses the possibility of producing non-survey based regional Social Accounting Matrices that may eventually allow the user to carry out impact analyses such as those of rural development policies, among others. The analysis is carried out for 12 selected European regions based on clusters.

    Keywords: Social accounting matrices, rural development, European regions, impact analysis.

    Pages: 319–346

    DOI: 10.2436/20.8080.02.62

  • Abstract: Aging societies have given rise to important challenges in the field of health insurance. Elderly policyholders need to be provided with fair premiums based on their individual health status, whereas insurance companies want to plan for the potential costs of tackling lifetimes above mean expectations. In this article, we focus on a large cohort of policyholders in Barcelona (Spain), aged 65 years and over. A shared-parameter joint model is proposed to analyse the relationship between annual demand for emergency claims and time until death outcomes, which are subject to left truncation. We compare different functional forms of the association between both processes, and, furthermore, we illustrate how the fitted model provides time-dynamic predictions of survival probabilities. The parameter estimation is performed under the Bayesian framework using Markov chain Monte Carlo methods.

    Keywords: Joint models, panel count data, left truncation, Bayesian framework, health insurance.


    DOI: 10.2436/20.8080.02.63

  • Abstract: Catastrophe bonds are financial instruments designed to transfer risk of monetary losses arising from earthquakes, hurricanes, or floods to the capital markets. The insurance and reinsurance industry, governments, and private entities employ them frequently to obtain coverage. Parametric catastrophe bonds base their payments on physical features. For instance, given parameters such as magnitude of the earthquake and the location of its epicentre, the bond may pay a fixed amount or not pay at all. This paper reviews statistical and machine learning techniques for designing trigger mechanisms and includes a computational experiment. Several lines of future research are discussed.

    Keywords: Catastrophe bonds, risk of natural hazards, classification techniques, earthquakes, insurance.

    Pages: 373–392

    DOI: 10.2436/20.8080.02.64

  • Abstract: Since its appearance in the 1990s, horizontal collaboration (HC) practices have revealed themselves as catalyzers for optimizing the distribution of goods in freight transport logistics. After introducing the main concepts related to HC, this paper offers a literature review on the topic and provides a classification of best practices in HC. Then, the paper analyses the main benefits and optimization challenges associated with the use of HC at the strategic, tactical, and operational levels. Emerging trends such as the concept of ‘green’ or environmentally-friendly HC in freight transport logistics are also introduced. Finally, the paper discusses the need of using hybrid optimization methods, such as simheuristics and learnheuristics, in solving some of the previously identified challenges in real-life scenarios dominated by uncertainty and dynamic conditions.

    Keywords: Horizontal collaboration, freight transport, sustainable logistics, supply chain management, combinatorial optimization.

    Pages: 393–414

    DOI: 10.2436/20.8080.02.65

Volume 41 (1), January-June 2017

  • Abstract: In the context of capture-recapture studies, Chao (1987) derived an inequality among capture frequency counts to obtain a lower bound for the size of a population based on individuals’ capture/non-capture records for multiple capture occasions. The inequality has been applied to obtain a non-parametric lower bound of species richness of an assemblage based on species incidence (detection/non-detection) data in multiple sampling units. The inequality implies that the number of undetected species can be inferred from the species incidence frequency counts of the uniques (species detected in only one sampling unit) and duplicates (species detected in exactly two sampling units). In their pioneering paper, Colwell and Coddington (1994) gave the name “Chao2” to the estimator for the resulting species richness. (The “Chao1” estimator refers to a similar type of estimator based on species abundance data). Since then, the Chao2 estimator has been applied to many research fields and led to fruitful generalizations. Here, we first review Chao’s inequality under various models and discuss some related statistical inference questions: (1) Under what conditions is the Chao2 estimator an unbiased point estimator? (2) How many additional sampling units are needed to detect any arbitrary proportion (including 100%) of the Chao2 estimate of asymptotic species richness? (3) Can other incidence frequency counts be used to obtain similar lower bounds? We then show how the Chao2 estimator can be also used to guide a non-asymptotic analysis in which species richness estimators can be compared for equally-large or equally-complete samples via sample-size-based and coverage-based rarefaction and extrapolation. We also review the generalization of Chao’s inequality to estimate species richness under other sampling-without-replacement schemes (e.g. a set of quadrats, each surveyed only once), to obtain a lower bound of undetected species shared between two or multiple assemblages, and to allow inferences about undetected phylogenetic richness (the total length of undetected branches of a phylogenetic tree connecting all species), with associated rarefaction and extrapolation. A small empirical dataset for Australian birds is used for illustration, using online software SpadeR, iNEXT, and PhD.

    Keywords: Cauchy-Schwarz inequality, Chao2 estimator, extrapolation, Good-Turing frequency, formula, incidence data, phylogenetic diversity, rarefaction, sampling effort, shared species richness, species richness.

    Pages: 3– 54

    DOI: 10.2436/20.8080.02.49

  • Abstract: The Lorenz curve is the most widely used graphical tool for describing and comparing inequality of income distributions. In this paper, we show that the elasticity of this curve is an indicator of the effect, in terms of inequality, of a truncation of the income distribution. As an application, we consider tax returns as equivalent to the truncation from below of a hypothetical income distribution. Then, we replace this hypothetical distribution by the income distribution obtained from a general household survey and use the dual Lorenz curve to anticipate this effect.

    Keywords Lorenz curve, tax data, truncation, inequality.

    Pages: 55– 72

    DOI: 10.2436/20.8080.02.50

  • Abstract: The Cox proportional hazards model is the most widely used survival prediction model for analysing time-to-event data. To measure the discrimination ability of a survival model the concordance probability index is widely used. In this work we studied and compared the performance of two different estimators of the concordance probability when a continuous predictor variable is categorised in a Cox proportional hazards regression model. In particular, we compared the c-index and the concordance probability estimator. We evaluated the empirical performance of both estimators through simulations. To categorise the predictor variable we propose a methodology which considers the maximal discrimination attained for the categorical variable. We applied this methodology to a cohort of patients with chronic obstructive pulmonary disease, in particular, we categorised the predictor variable forced expiratory volume in one second in percentage.

    Keywords: Categorisation, prediction models, cutpoint, Cox model.

    Pages: 73– 92

    DOI: 10.2436/20.8080.02.51

  • Abstract: Cultivation of horticultural species under organic management has increased in importance in recent years. However, the sustainability of this new production method needs to be supported by scientific research, especially in the field of virology. We studied the prevalence of three important virus diseases in agroecosystems with regard to its management system: organic versus non-organic, with and without greenhouse. Prevalence was assessed by means of a Bayesian correlated binary model which connects the risk of infection of each virus within the same plot and was defined in terms of a logit generalized linear mixed model (GLMM). Model robustness was checked through a sensitivity analysis based on different hyperprior scenarios. Inferential results were examined in terms of changes in the marginal posterior distributions, both for fixed and for random effects, through the Hellinger distance and a derived measure of sensitivity. Statistical results suggested that organic systems show lower or similar prevalence than non-organic ones in both single and multiple infections as well as the relevance of the prior specification of the random effects in the inferential process.

    Keywords: Hellinger distance, model robustness, risk infection, sensitivity analysis, virus epidemiology.

    Pages: 93– 116

    DOI: 10.2436/20.8080.02.52

  • Pages: 117– 118

    DOI: 10.2436/20.8080.02.53

  • Abstract: In this paper we study a goodness-of-fit test based on the maximum correlation coefficient, in the context of randomly censored data. We construct a new test statistic under general right- censoring and prove its asymptotic properties. Additionally, we study a special case, when the censoring mechanism follows the well-known Koziol-Green model. We present an extensive simulation study on the empirical power of these two versions of the test statistic, showing their ad- vantages over the widely used Pearson-type test. Finally, we apply our test to the head-and-neck cancer data.

    Keywords: Goodness-of-fit, Kaplan-Meier estimator, maximum correlation, random censoring.

    Pages: 119– 138

    DOI: 10.2436/20.8080.02.54

  • Abstract: Methods to preserve confidentiality when publishing geographic information conflict with the need to publish accurate data. The goal of this paper is to create a European geographic grid frame- work to disseminate statistical data over maps. We propose a methodology based on quadtree hierarchical geographic data structures. We create a varying size grid adapted to local area densities. High populated zones are disaggregated in small squares to allow dissemination of accurate data. Alternatively, information on low populated zones is published in big squares to avoid identification of individual data. The methodology has been applied to the 2014 population register data in Catalonia.

    Keywords: Official statistics, confidentiality, disclosure limitation, dissemination, geographic information systems, hierarchical data structures, small area geography.

    Pages: 139– 158

    DOI: 10.2436/20.8080.02.55

  • Abstract: Our objective in this paper is to model the dynamics of respiratory syncytial virus in the region of Valencia (Spain) and analyse the effect of vaccination strategies from a health-economic point of view. Compartmental mathematical models based on differential equations are commonly used in epidemiology to both understand the underlying mechanisms that influence disease transmission and analyse the impact of vaccination programs. However, a recently proposed Bayesian stochastic susceptible-infected-recovered-susceptible model in discrete-time provided an improved and more natural description of disease dynamics. In this work, we propose an extension of that stochastic model that allows us to simulate and assess the effect of a vaccination strategy that consists on vaccinating a proportion of newborns.

    Keywords: Infectious diseases, respiratory syncytial virus (RSV), discrete-time epidemic model, stochastic compartmental model, Bayesian analysis, intervention strategies.

    Pages: 159– 176

    DOI: 10.2436/20.8080.02.56

  • Abstract: Regression models for counts could be applied to the earth sciences, for instance when studying trends of extremes of climatological quantities. Hurdle models are modified count models which can be regarded as mixtures of distributions. In this paper, hurdle models are applied to model the sums of lengths of periods of high temperatures. A modification to the common versions presented in the literature is presented, as left truncation as well as a particular treatment of zeros is needed for the problem. The outcome of the model is compared to those of simpler count models.

    Keywords: Count data, hurdle models, Poisson regression, negative binomial distribution, climate.

    Pages: 177– 188

    DOI: 10.2436/20.8080.02.57

Volume 40 (2), July-December 2016

  • Abstract: The simple assembly line balancing problem type E (abbreviated as SALBP-E) occurs when the number of workstations and the cycle time are variables and the objective is to maximise the line efficiency. In contrast with other types of SALBPs, SALBP-E has received little attention in the literature. In order to solve optimally SALBP-E, we propose a mixed integer liner programming model and an iterative procedure. Since SALBP-E is NP-hard, we also propose heuristics derived from the aforementioned procedures for solving larger instances. An extensive experimentation is carried out and its results show the improvement of the SALBP-E resolution.

    Keywords: Assembly line balancing, SALBP, manufacturing optimisation.

    Pages: 227– 242

    DOI: 10.2436/20.8080.02.42

  • Abstract: This article is directed at the problem of reliability estimation using ranked set sampling. A nonparametric estimator based on kernel density estimation is developed. The estimator is shown to be superior to its analog in simple random sampling. Monte Carlo simulations are employed to assess performance of the proposed estimator. Two real data sets are analysed for illustration.

    Keywords: Bandwidth selection, Judgment ranking, Stress-strength model.

    Pages: 243– 266

    DOI: 10.2436/20.8080.02.43

  • Abstract: We present a construction of a family of continuous-time ARMA processes based on p iterations of the linear operator that maps a Lévy process onto an Ornstein-Uhlenbeck process. The construction resembles the procedure to build an AR(p) from an AR(1). We show that this family is in fact a subfamily of the well-known CARMA(p,q) processes, with several interesting advantages, including a smaller number of parameters. The resulting processes are linear combinations of Ornstein-Uhlenbeck processes all driven by the same Lévy process. This provides a straightforward computation of covariances, a state-space model representation and methods for estimating parameters. Furthermore, the discrete and equally spaced sampling of the process turns to be an ARMA(p, p−1) process. We propose methods for estimating the parameters of the iterated Ornstein-Uhlenbeck process when the noise is either driven by a Wiener or a more general Lévy process, and show simulations and applications to real data.

    Keywords: Ornstein-Uhlenbeck process, Lévy process, Continuous ARMA, stationary process.

    Pages: 267– 302

    DOI: 10.2436/20.8080.02.44

  • Abstract: The possibilities of the use of the coefficient of variation over a high threshold in tail modelling are discussed. The paper also considers multiple threshold tests for a generalized Pareto distribution, together with a threshold selection algorithm. One of the main contributions is to extend the methodology based on moments to all distributions, even without finite moments. These techniques are applied to euro/dollar daily exchange rates and to Danish fire insurance losses.

    Keywords: Statistics of extremes, heavy tails, high quantile estimation, value at risk.

    Pages: 303– 320

    DOI: 10.2436/20.8080.02.45

  • Abstract: This study proposes two methods for detecting outliers in functional time series. Both methods take dependence in the data into account and are based on robust functional principal component analysis. One method seeks outliers in the series of projections on the first principal component. The other obtains uncontaminated forecasts for each data set and determines that those observations whose residuals have an unusually high norm are considered outliers. A simulation study shows the performance of these proposed procedures and the need to take dependence in the time series into account. Finally, the usefulness of our methodology is illustrated in two real datasets from the electricity market: daily curves of electricity demand and price in mainland Spain, for the year 2012.

    Keywords: Functional data analysis, functional principal component analysis, functional time series, outlier detection, electricity demand and price.

    Pages: 321– 348

    DOI: 10.2436/20.8080.02.46

  • Abstract: When traditional methods are applied to compositional data misleading and incoherent results could be obtained. Finite mixtures of multivariate distributions are becoming increasingly important nowadays. In this paper, traditional strategies to fit a mixture model into compositional data sets are revisited and the major difficulties are detailed. A new proposal using a mixture of distributions defined on orthonormal log-ratio coordinates is introduced. A real data set analysis is presented to illustrate and compare the different methodologies.

    Keywords: Compositional data, Finite Mixture, Log ratio, Model-based clustering, Normal distribution, Orthonormal coordinates, Simplex.

    Pages: 340– 374

    DOI: 10.2436/20.8080.02.47

  • Abstract: One important goal in clinical applications of multi-state models is the estimation of transition probabilities. Recently, landmark estimators were proposed to estimate these quantities, and their superiority with respect to the competing estimators has been proved in situations in which the Markov condition is violated. As a weakness, it provides large standard errors in estimation in some circumstances. In this article, we propose two approaches that can be used to reduce the variability of the proposed estimator. Simulations show that the proposed estimators may be much more efficient than the unsmoothed estimator. A real data illustration is included.

    Keywords: Kaplan-Meier, Multi-state model, Nonparametric estimation, Presmoothing, Survival Analysis.

    Pages: 375– 398

    DOI: 10.2436/20.8080.02.48

Volume 40 (1), January-June 2016

  • Abstract: As part of national accounts, input-output tables are becoming crucial statistical tools to study the economic, social and environmental impacts of globalization and international trade. In particular, global input-output tables extend the national dimension to the international dimension by relating individual countries’ input-output tables among each other, thus providing an opportunity to balance the global economy as a whole. Concerning emissions of greenhouse gases, the relative position that countries hold among their main trade partners at the global level is a key issue in terms of international climate negotiations. With this purpose, we show that (official) Multi-country input-output tables are crucial to analyse the greenhouse gas emission trade balance of individual countries. Spain has a negative trade emissions balance for all three gases analysed, being the most negative balances those associated to the bilateral trade with China, Russia, United States and the rest of the European Union as a whole.

    Keywords: WIOD, Emissions Trade Balance, Spain, GHG footprint, GHG.

    Pages: 3– 30

    DOI: 10.2436/20.8080.02.33

  • Abstract: In this paper two alternative estimation procedures based on the EM algorithm are proposed for the flexible negative binomial cure rate model with a latent activation scheme. The Weibull model as well as the log-normal and gamma distributions are also considered for the time-to-event data for the non-destroyed cells. Simulation studies show the satisfactory performance of the proposed methodology. The impact of misspecifying the survival function on both components of the model (cured and susceptible) is also evaluated. The use of the new methodology is illustrated with a real data set related to a clinical trial on Phase III cutaneous melanoma patients.

    Keywords: Competing risks, EM algorithm, latent activation scheme.

    Pages: 31–54

    DOI: 10.2436/20.8080.02.34

  • Abstract: In this paper, a goodness-of-fit test for normality based on the comparison of the theoretical and empirical distributions is proposed. Critical values are obtained via Monte Carlo for several sample sizes and different significance levels.We study and compare the power of forty selected normality tests for a wide collection of alternative distributions. The new proposal is compared to some traditional test statistics, such as Kolmogorov-Smirnov, Kuiper, Cramér-von Mises, Anderson-Darling, Pearson Chi-square, Shapiro-Wilk, Shapiro-Francia, Jarque-Bera, SJ, Robust Jarque-Bera, and also to entropy-based test statistics. From the simulation study results it is concluded that the best performance against asymmetric alternatives with support on the whole real line and alternative distributions with support on the positive real line is achieved by the new test. Other findings derived from the simulation study are that SJ and Robust Jarque-Bera tests are the most powerful ones for symmetric alternatives with support on the whole real line, whereas entropy-based tests are preferable for alternatives with support on the unit interval.

    Keywords: Empirical distribution function, entropy estimator, goodness-of-fit tests, Monte Carlo simulation, Robust Jarque-Bera test, Shapiro-Francia test, SJ test, test for normality.

    Pages: 55–88

    DOI: 10.2436/20.8080.02.35

  • Abstract: In this paper, based on record data from the two-parameter logistic distribution, the maximum likelihood and Bayes estimators for the two unknown parameters are derived. The maximum likelihood estimators and Bayes estimators can not be obtained in explicit forms. We present a simple method of deriving explicit maximum likelihood estimators by approximating the likelihood function. Also, an approximation based on the Gibbs sampling procedure is used to obtain the Bayes estimators. Asymptotic confidence intervals, bootstrap confidence intervals and credible intervals are also proposed. Monte Carlo simulations are performed to compare the performances of the different proposed methods. Finally, one real data set has been analysed for illustrative purposes.

    Keywords: Logistic distribution, record data,maximum likelihood estimator, Bayes estimator, Gibbs sampling.

    Pages: 89–112

    DOI: 10.2436/20.8080.02.36

  • Abstract: Bivariate count data arise in several different disciplines and the bivariate Poisson distribution is commonly used to model them. This paper proposes and studies a computationally convenient goodness-of-fit test for this distribution, which is based on an empirical counterpart of a system of equations. The test is consistent against fixed alternatives. The null distribution of the test can be consistently approximated by a parametric bootstrap and by a weighted bootstrap. The goodness of these bootstrap estimators and the power for finite sample sizes are numerically studied. It is shown that the proposed test can be naturally extended to the multivariate Poisson distribution.

    Keywords: Bivariate Poisson distribution, goodness-of-fit, empirical probability generating function, parametric bootstrap, weighted bootstrap, multivariate Poisson distribution.

    Pages: 113–138

    DOI: 10.2436/20.8080.02.37

  • Abstract: Tigernut tubers are the main ingredient in the production of orxata in Valencia, a white soft sweet popular drink. In recent years, the appearance of black spots in the skin of tigernuts has led to important economic losses in orxata production because severely diseased tubers must be discarded. In this paper, we discuss three complementary statistical models to assess the disease incidence of harvested tubers from selected or treated seeds, and propose a measure of effectiveness for different treatments against the disease based on the probability of germination and the incidence of the disease. Statistical methods for these studies are approached from Bayesian reasoning and include mixed-effects models, Dirichlet-multinomial inferential processes and mixed-effects logistic regression models. Statistical analyses provide relevant information to carry out measures to palliate the black spot disease and achieve a high-quality production. For instance, the study shows that avoiding affected seeds increases the probability of harvesting asymptomatic tubers. It is also revealed that the best chemical treatment, when prioritizing germination, is disinfection with hydrochloric acid while sodium hypochlorite performs better if the priority is to have a reduced disease incidence. The reduction of the incidence of the black spots syndrome by disinfection with chemical agents supports the hypothesis that the causal agent is a pathogenic organism.

    Keywords: Dirichlet-multinomial model, logistic regression, measures of effectiveness, tigernuts tubers.

    Pages: 139–152

    DOI: 10.2436/20.8080.02.38

  • Abstract: A two-parameter transmuted geometric distribution is proposed as a new generalization of the geometric distribution by employing the quadratic transmutation techniques of Shaw and Buckley. The additional parameter plays the role of controlling the tail length. Distributional properties of the proposed distribution are investigated. Maximum likelihood estimation method is discussed along with some data fitting experiments to show its advantages over some existing distributions in literature. The tail flexibility of density of aggregate loss random variable assuming the proposed distribution as primary distribution is outlined and presented along with a illustrative modelling of aggregate claim of a vehicle insurance data. Finally, we present a count regression model based on the proposed distribution and carry out its comparison with some established models.

    Keywords: Aggregate claim, count regression, geometric distribution, transmuted distribution.

    Pages: 153–176

    DOI: 10.2436/20.8080.02.39

  • Abstract: Motivated by three failure data sets (lifetime of patients, failure time of hard drives and failure time of a product), we introduce three different three-parameter distributions, study basic mathematical properties, address estimation by the method of maximum likelihood and investigate finite sample performance of the estimators. We show that one of the new distributions provides a better fit to each data set than eight other distributions each having three parameters and three distributions each having two parameters.

    Keywords: Linear failure rate distribution, maximum likelihood estimation, Poisson distribution.

    Pages: 177–200

    DOI: 10.2436/20.8080.02.40

  • Abstract: Metaheuristics are approximation methods used to solve combinatorial optimization problems. Their performance usually depends on a set of parameters that need to be adjusted. The selection of appropriate parameter values causes a loss of efficiency, as it requires time, and advanced analytical and problem-specific skills. This paper provides an overview of the principal approaches to tackle the Parameter Setting Problem, focusing on the statistical procedures employed so far by the scientific community. In addition, a novel methodology is proposed, which is tested using an already existing algorithm for solving the Multi-Depot Vehicle Routing Problem.

    Keywords: Parameter fine-tuning, metaheuristics, statistical learning, biased randomization.

    Pages: 201–224

    DOI: 10.2436/20.8080.02.41

Volume 39 (2), July-December 2015

  • Abstract: P-splines first appeared in the limelight twenty years ago. Since then they have become popular in applications and in theoretical work. The combination of a rich B-spline basis and a simple difference penalty lends itself well to a variety of generalizations, because it is based on regression. In effect, P-splines allow the building of a “backbone” for the “mixing and matching” of a variety of additive smooth structure components, while inviting all sorts of extensions: varying-coefficient effects, signal (functional) regressors, two-dimensional surfaces, non-normal responses, quantile (expectile) modelling, among others. Strong connections with mixed models and Bayesian analysis have been established. We give an overview of many of the central developments during the first two decades of P-splines.

    Keywords: B-splines, penalty, additive model, mixed model, multidimensional smoothing.

    Pages: 149–186

    DOI: 10.2436/20.8080.02.25

  • Abstract: In this paper we investigate an extension of the power-normal model, called the alpha-power model and specialize it to linear and nonlinear regression models, with and without correlated errors. Maximum likelihood estimation is considered with explicit derivation of the observed and expected Fisher information matrices. Applications are considered for the Australian athletes data set and also to a data set studied in Xie et al. (2009). The main conclusion is that the proposed model can be a viable alternative in situations were the normal distribution is not the most adequate model.

    Keywords: Correlation, maximum likelihood, power-normal distribution, regression.

    Pages: 187–208

    DOI: 10.2436/20.8080.02.26

  • Abstract: The Sarmanov family of distributions can provide a good model for bivariate random variables and it is used to model dependency in a multivariate setting with given marginals. In this paper, we focus our attention on the bivariate Sarmanov distribution and copula with different truncated extreme value marginal distributions. We compare a global estimation method based on maximizing the full log-likelihood function with the estimation based on maximizing the pseudo-log-likelihood function for copula (or partial estimation). Our aim is to estimate two statistics that can be used to evaluate the risk of the sum exceeding a given value. Numerical results using a real data set from the motor insurance sector are presented.

    Keywords: Bivariate Sarmanov distribution, truncated marginal distributions, copula representation, risk measures.

    Pages: 209–230

    DOI: 10.2436/20.8080.02.27

  • Abstract: Social polices are designed using information collected in surveys; such as the Catalan Time Use survey. Accurate comparisons of time use data among population groups are commonly analysed using statistical methods. The total daily time expended on different activities by a single person is equal to 24 hours. Because this type of data are compositional, its sample space has particular properties that statistical methods should respect. The critical points required to interpret differences between groups are provided and described in terms of log-ratio methods. These techniques facilitate the interpretation of the relative differences detected in multivariate and univariate analysis.

    Keywords: Log-ratio transformations, MANOVA, perturbation, simplex, subcomposition.

    Pages: 231–252

    DOI: 10.2436/20.8080.02.28

  • Abstract: Recent years have seen an increase in the development of robust approaches for stochastic project management methodologies such as PERT (Program Evaluation and Review Technique). These robust approaches allow for elevated likelihoods of outlying events, thereby widening interval estimates of project completion times. However, little attention has been paid to the fact that outlying events and/or expert judgments may be asymmetric. We propose the tilted beta distribution which permits both elevated likelihoods of outlying events as well as an asymmetric representation of these events. We examine the use of the tilted beta distribution in PERT with respect to other project management distributions.

    Keywords: Activity times, finite mixture, PERT, tilted beta distribution, robust project management, sensitivity analysis.

    Pages: 253–272

    DOI: 10.2436/20.8080.02.29

  • Abstract: In a recent edition of SORT, Bidram and Nekoukhou proposed a novel class of distributions and derived its mathematical properties. Several of the mathematical properties are expressed as single infinite sums or double infinite sums. Here, we show that many of these properties can be expressed in terms of known special functions, functions for which in-built routines are widely available.

    Keywords: Double bounded Kumaraswamy-power series class of distributions, Fox Wright generalized, hypergeometric function, generalized hypergeometric function.

    Pages: 273–280

    DOI: 10.2436/20.8080.02.30

  • Abstract: Generalized linear mixed models are flexible tools for modeling non-normal data and are useful for accommodating overdispersion in Poisson regression models with random effects. Their main difficulty resides in the parameter estimation because there is no analytic solution for the maximization of the marginal likelihood. Many methods have been proposed for this purpose and many of them are implemented in software packages. The purpose of this study is to compare the performance of three different statistical principles —marginal likelihood, extended likelihood, Bayesian analysis— via simulation studies. Real data on contact wrestling are used for illustration.

    Keywords: Estimation methods, overdispersion, Poisson generalized linear mixed models, simulation study, statistical principles, sport injuries.

    Pages: 281–308

    DOI: 10.2436/20.8080.02.31

  • Abstract: We consider estimation techniques from dual frame surveys in the case of estimation of proportions when the variable of interest has multinomial outcomes. We propose to describe the joint distribution of the class indicators by a multinomial logistic model. Logistic generalized regression estimators and model calibration estimators are introduced for class frequencies in a population. Theoretical asymptotic properties of the proposed estimators are shown and discussed. Monte Carlo experiments are also carried out to compare the efficiency of the proposed procedures for finite size samples and in the presence of different sets of auxiliary variables. The simulation studies indicate that the multinomial logistic formulation yields better results than the classical estimators that implicitly assume individual linear models for the variables. The proposed methods are also applied in an attitude survey.

    Keywords: Finite population, survey sampling, auxiliary information, model assisted inference, calibration.

    Pages: 309–336

    DOI: 10.2436/20.8080.02.32

Volume 39 (1), January-June 2015

  • Abstract: The Weibull distribution is a very applicable model for lifetime data. In this paper, we have investigated inference on the parameters of Weibull distribution based on record values. We first propose a simple and exact test and a confidence interval for the shape parameter. Then, in addition to a generalized confidence interval, a generalized test variable is derived for the scale parameter when the shape parameter is unknown. The paper presents a simple and exact joint confidence region as well. In all cases, simulation studies show that the proposed approaches are more satisfactory and reliable than previous methods. All proposed approaches are illustrated using a real example.

    Keywords: Coverage probability, generalized confidence interval, generalized p-value, records, Weibull distribution.

    Pages: 3–18

    DOI: 10.2436/20.8080.02.17

  • Abstract: his paper deals with small area estimation of poverty indicators. Small area estimators of these quantities are derived from partitioned time-dependent area-level linear mixed models. The introduced models are useful for modelling the different behaviour of the target variable by sex or any other dichotomic characteristic. The mean squared errors are estimated by explicit formulas. An application to data from the Spanish Living Conditions Survey is given.

    Keywords: Area-level models, small area estimation, time correlation, poverty indicators.

    Pages: 19–34

    DOI: 10.2436/20.8080.02.18

  • Abstract: In this paper we study a new class of skew-Cauchy distributions inspired on the family extended two-piece skew normal distribution. The new family of distributions encompasses three well known families of distributions, the normal, the two-piece skew-normal and the skew-normal-Cauchy distributions. Some properties of the new distribution are investigated, inference via maximum likelihood estimation is implemented and results of a real data application, which reveal good performance of the new model, are reported.ious methods. All proposed approaches are illustrated using a real example.

    Keywords: Cauchy distribution, kurtosis, maximum likelihood estimation, singular information matrix, skewness, Skew-Normal-Cauchy distribution.

    Pages: 35–50

    DOI: 10.2436/20.8080.02.19

  • Abstract: High leverage collinearity influential observations are those high leverage points that change the multicollinearity pattern of a data. It is imperative to identify these points as they are responsible for misleading inferences on the fitting of a regression model. Moreover, identifying these observations may help statistics practitioners to solve the problem of multicollinearity, which is caused by high leverage points. A diagnostic plot is very useful for practitioners to quickly capture abnormalities in a data. In this paper, we propose new diagnostic plots to identify high leverage collinearity influential observations. The merit of our proposed diagnostic plots is confirmed by some well-known examples and Monte Carlo simulations.

    Keywords: Collinearity influential observation, diagnostic robust generalized potential, high lever-age points, multicollinearity.

    Pages: 51–70

    DOI: 10.2436/20.8080.02.20

  • Abstract: Classical discrete distributions rarely support modelling data on the set of whole integers. In this paper, we shall introduce a flexible discrete distribution on this set, which can, in addition, cover bimodal as well as unimodal data sets. The proposed distribution can also be fitted to positive and negative skewed data. The distribution is indeed a discrete counterpart of the continuous alpha-skew-Laplace distribution recently introduced in the literature. The proposed distribution can also be viewed as a weighted version of the discrete Laplace distribution. Several distributional properties of this class such as cumulative distribution function, moment generating function, moments, modality, infinite divisibility and its truncation are studied. A simulation study is also performed. Finally, a real data set is used to show applicability of the new model comparing to several rival models, such as the discrete normal and Skellam distributions.

    Keywords: Discrete Laplace distribution, discretization, maximum likelihood estimation, uni-bimodality, weighted distribution.

    Pages: 71–84

    DOI: 10.2436/20.8080.02.21

  • Abstract: The analysis of markets with indivisible goods and fixed exogenous prices has played an important role in economic models, especially in relation to wage rigidity and unemployment. This paper provides a novel mathematical programming based approach to study pure exchange economies where discrete amounts of commodities are exchanged at fixed prices. Barter processes, consisting in sequences of elementary reallocations of couple of commodities among couples of agents, are formalized as local searches converging to equilibrium allocations. A direct application of the analysed processes in the context of computational economics is provided, along with a Java implementation of the described approaches.

    Keywords: Numerical optimization, combinatorial optimization, microeconomic theory.

    Pages: 85–108

    DOI: 10.2436/20.8080.02.22

  • Abstract: Likelihood estimates of the Dirichlet distribution parameters can be obtained only through numerical algorithms. Such algorithms can provide estimates outside the correct range for the parameters and/or can require a large amount of iterations to reach convergence. These problems can be aggravated if good starting values are not provided. In this paper we discuss several approaches that can partially avoid these problems providing a good trade-off between efficiency and stability. The performances of these approaches are compared on high-dimensional real and simulated data.

    Keywords: Levenberg-Marquardt algorithm, re-parametrization, starting values, metabolomics data.

    Pages: 109–126

    DOI: 10.2436/20.8080.02.23

  • Abstract: In this paper, the exponentiated discrete Weibull distribution is introduced. This new generalization of the discrete Weibull distribution can also be considered as a discrete analogue of the exponentiated Weibull distribution. A special case of this exponentiated discrete Weibull distribution defines a new generalization of the discrete Rayleigh distribution for the first time in the literature. In addition, discrete generalized exponential and geometric distributions are some special sub-models of the new distribution. Here, some basic distributional properties, moments, and order statistics of this new discrete distribution are studied. We will see that the hazard rate function can be in- creasing, decreasing, bathtub, and upside-down bathtub shaped. Estimation of the parameters is illustrated using the maximum likelihood method. The model with a real data set is also examined.

    Keywords: Discrete generalized exponential distribution, exponentiated discrete Weibull distribution, exponentiated Weibull distribution, geometric distribution, infinite divisibility, order statistics, resilience parameter family, stress-strength parameter.

    Pages: 127–146

    DOI: 10.2436/20.8080.02.24

Volume 38, number 2 (July–December 2014)

Volume 38, number 1 (January–June 2014)

Volume 37, number 2 (July–December 2013)

Volume 37, number 1 (January–June 2013)

Volume 36, number 2 (July–December 2012)

Volume 36, number 1 (January–June 2012)

Volume 35, number 2 (July–December 2011)

Special issue: Privacy in statistical databases. September 2011

Volume 35, number 1 (January–June 2011)

Volume 34, number 2 (July–December 2010)

Volume 34, number 1 (January–June 2010)

Volume 33, number 2 (July–December 2009)

Volume 33, number 1 (January–June 2009)

Volume 32, number 2 (July–December 2008)

Volume 32, number 1 (January–June 2008)

Volume 31, number 2 (July–December 2007)

Volume 31, number 1 (January–June 2007)

Special issue. Albert Prat in memoriam (April 2006)

Albert Prat i la docència

Albert Prat i l'estadística

Alguns articles publicats per Albert Prat

Volume 30, number 2 (July–December 2006)

Volume 30, number 1 (January–June 2006)

Volume 29, number 2 (July–December 2005)

Volume 29, number 1 (January–June 2005)

Volume 27, number 2 (July–December 2003)

Volume 27, number 1 (January–June 2003)