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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.
Pages:347–372
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
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
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
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
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
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