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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
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
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
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
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