DSpace Angular :: Browsing by Author "Arellano Valle, Reinaldo B."

Browsing by Author "Arellano Valle, Reinaldo B."

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A formulation for continuous mixtures of multivariate normal distributions
(ELSEVIER INC, 2021) Arellano Valle, Reinaldo B.; Azzalini, Adelchi
Several formulations have long existed in the literature in the form of continuous mixtures of normal variables where a mixing variable operates on the mean or on the variance or on both the mean and the variance of a multivariate normal variable, by changing the nature of these basic constituents from constants to random quantities. More recently, other mixture-type constructions have been introduced, where the core random component, on which the mixing operation operates, is not necessarily normal. The main aim of the present work is to show that many existing constructions can be encompassed by a formulation where normal variables are mixed using two univariate random variables. For this formulation, we derive various general properties, with focus on the multivariate context. Within the proposed framework, it is also simpler to formulate new proposals of parametric families, and we provide a few such instances. As a side product, the exposition provides a concise compendium of the main constructions of continuous normal-mixtures type, although a full overview of this vast theme is not attempted. (C) 2021 Published by Elsevier Inc.
A multivariate ultrastructural errors-in-variables model with equation error
(ELSEVIER INC, 2011) Patriota, Alexandre G.; Bolfarine, Heleno; Arellano Valle, Reinaldo B.
This paper deals with asymptotic results on a multivariate ultrastructural errors-in-variables regression model with equation errors Sufficient conditions for attaining consistent estimators for model parameters are presented Asymptotic distributions for the line regression estimators are derived Applications to the elliptical class of distributions with two error assumptions are presented The model generalizes previous results aimed at univariate scenarios (C) 2010 Elsevier Inc All rights reserved
A unified view on skewed distributions arising from selections
(WILEY, 2006) Arellano Valle, Reinaldo B.; Branco, Marcia D.; Genton, Marc G.
Parametric families of multivariate nonnormal distributions have received considerable attention in the past few decades. The authors propose a new definition of a selection distribution that encompasses many existing families of multivariate skewed distributions. Their work is motivated by examples that involve various forms of selection mechanisms and lead to skewed distributions. They give the main properties of selection distributions and show how various families of multivariate skewed distributions, such as the skew-normal and skew-elliptical distributions, arise as special cases. The authors further introduce several methods of constructing selection distributions based on linear and nonlinear selection mechanisms.
An Extension of the Epsilon-Skew-Normal Distribution
(TAYLOR & FRANCIS INC, 2010) Arellano Valle, Reinaldo B.; Cortes, Milton A.; Gomez, Hector W.
This article is related with the probabilistic and statistical properties of an parametric extension of the so-called epsilon-skew-normal (ESN) distribution introduced by Mudholkar and Hutson (2000), which considers an additional shape parameter in order to increase the flexibility of the ESN distribution. Also, this article concerns likelihood inference about the parameters of the new class. In particular, the information matrix of the maximum likelihood estimators is obtained, showing that it is non singular in the special normal case. Finally, the statistical methods are illustrated with two examples based on real datasets.
An Extension to the Scale Mixture of Normals for Bayesian Small-Area Estimation
(UNIV NAC COLOMBIA, DEPT ESTADISTICA, 2012) Torres Aviles, Francisco J.; Icaza, Gloria; Arellano Valle, Reinaldo B.
This work considers distributions obtained as scale mixture of normal densities for correlated random variables, in the context of the Markov random field theory, which is applied in Bayesian spatial intrinsically autoregressive random effect models. Conditions are established in order to guarantee the posterior distribution existence when the random field is assumed as scale mixture of normal densities. Lung, trachea and bronchi cancer relative risks and childhood diabetes incidence in Chilean municipal districts are estimated to illustrate the proposed methods. Results are presented using appropriate thematic maps. Inference over unknown parameters is discussed and some extensions are proposed.
Bayesian inference for dependent elliptical measurement error models
(ELSEVIER INC, 2010) Vidal, Ignacio; Arellano Valle, Reinaldo B.
In this article we provide a Bayesian analysis for dependent elliptical measurement error models considering nondifferential and differential errors. In both cases we compute posterior distributions for structural parameters by using squared radial prior distributions for the precision parameters. The main result is that the posterior distribution of location parameters, for specific priors, is invariant with respect to changes in the generator function, in agreement with previous results obtained in the literature under different assumptions. Finally, although the results obtained are valid for any elliptical distribution for the error term, we illustrate those results by using the student-t distribution and a real data set. (c) 2010 Elsevier Inc. All rights reserved.
Bayesian Inference for Shape Mixtures of Skewed Distributions, with Application to Regression Analysis
(INT SOC BAYESIAN ANALYSIS, 2008) Arellano Valle, Reinaldo B.; Castro, Luis M.; Genton, Marc G.; Gomez, Hector W.
We introduce a class of shape mixtures of skewed distributions and study some of its main properties. We discuss a Bayesian interpretation and some invariance results of the proposed class. We develop a Bayesian analysis of the skew-normal, skew-generalized-normal, skew-normal-t and skew-t-normal linear regression models under some special prior specifications for the model parameters. In particular, we show that the full posterior of the skew-normal regression model parameters is proper under an arbitrary proper prior for the shape parameter and noninformative prior for the other parameters. We implement a convenient hierarchical representation in order to obtain the corresponding posterior analysis. We illustrate our approach with an application to a real dataset on characteristics of Australian male athletes.
Bayesian Modeling of Censored Partial Linear Models using Scale-Mixtures of Normal Distributions
(AMER INST PHYSICS, 2012) Castro, Luis M.; Lachos, Victor H.; Ferreira, Guillermo P.; Arellano Valle, Reinaldo B.; Stern, JM; Lauretto, MD; Polpo, A; Diniz, MA
Regression models where the dependent variable is censored (limited) are usually considered in statistical analysis. Particularly, the case of a truncation to the left of zero and a normality assumption for the error terms is studied in detail by [1] in the well known Tobit model. In the present article, this typical censored regression model is extended by considering a partial linear model with errors belonging to the class of scale mixture of normal distributions. We achieve a fully Bayesian inference by adopting a Metropolis algorithm within a Gibbs sampler. The likelihood function is utilized to compute not only some Bayesian model selection measures but also to develop Bayesian case-deletion influence diagnostics based on the q-divergence measures. We evaluate the performances of the proposed methods with simulated data. In addition, we present an application in order to know what type of variables affect the income of housewives.
LIKELIHOOD BASED INFERENCE FOR SKEW-NORMAL INDEPENDENT LINEAR MIXED MODELS
(STATISTICA SINICA, 2010) Lachos, Victor H.; Ghosh, Pulak; Arellano Valle, Reinaldo B.
Linear mixed models with normally distributed response are routinely used in longitudinal data. However, the accuracy of the assumed normal distribution is crucial for valid inference of the parameters We present a new class of asymmetric linear mixed models that provides for an efficient estimation of the parameters in the analysis of longitudinal data We assume that, marginally. the random effects follow a multivariate skew-normal/independent distribution (Branco and Dey (2001)) and that the random errors follow a symmetric normal/independent distribution (Lange and Sinsheimer (1993)), providing an appealing robust alternative to the usual symmetric normal distribution in linear mixed models Specific distributions examined include the skew-normal, the skew-t, the skew-slash, and the skew-contaminated normal distribution We present all efficient EM-type algorithm algorithm for the computation of maximum likelihood estimation of parameters The technique for the prediction of future responses under this class of distributions is also investigated The methodology is illustrated through an applications to Framingham cholesterol data and a. simulation study.
On the exact distribution of linear combinations of order statistics from dependent random variables
(ELSEVIER INC, 2007) Arellano Valle, Reinaldo B.; Genton, Marc G.
We study the exact distribution of linear combinations of order statistics of arbitrary (absolutely continuous) dependent random variables. In particular, we examine the case where the random variables have a joint elliptically contoured distribution and the case where the random variables are exchangeable. We investigate also the particular L-statistics that simply yield a set of order statistics, and study their joint distribution. We present the application of our results to genetic selection problems, design of cellular phone receivers, and visual acuity. We give illustrative examples based on the multivariate normal and multivariate Student t distributions. (c) 2007 Elsevier Inc. All rights reserved.
On the exact distribution of the maximum of absolutely continuous dependent random variables
(ELSEVIER SCIENCE BV, 2008) Arellano Valle, Reinaldo B.; Genton, Marc G.
We derive the exact probability density function of the maximum of arbitrary absolutely continuous dependent random variables and of absolutely continuous exchangeable random variables. We show this density is related to the family of fundamental skew distributions. In particular, we examine the case where the random variables have an elliptically contoured distribution. We study some particular examples based on the multivariate normal and multivariate Student t distributions, and discuss numerical computation issues. We illustrate our results on a genetic selection problem and on an autoregressive time series model of order one. (C) 2007 Elsevier B.V. All rights reserved.
On the unification of families of skew-normal distributions
(BLACKWELL PUBLISHING, 2006) Arellano Valle, Reinaldo B.; Azzalini, Adelchi
The distribution theory literature connected to the multivariate skew-normal distribution has grown rapidly in recent years, and a number of extensions and alternative formulations have been put forward. Presently there are various coexisting proposals, similar but not identical, and with rather unclear connections. The aim of this paper is to unify these proposals under a new general formulation, clarifying at the same time their relationships. The final part sketches an extension of the argument to the skew-elliptical family.
Partially linear censored regression models using heavy-tailed distributions: A Bayesian approach
(ELSEVIER SCIENCE BV, 2014) Castro, Luis M.; Lachos, Victor H.; Ferreira, Guillermo P.; Arellano Valle, Reinaldo B.
Linear regression models where the response variable is censored are often considered in statistical analysis. A parametric relationship between the response variable and covariates and normality of random errors are assumptions typically considered in modeling censored responses. In this context, the aim of this paper is to extend the normal censored regression model by considering on one hand that the response variable is linearly dependent on some covariates whereas its relation to other variables is characterized by nonparametric functions, and on the other hand that error terms of the regression model belong to a class of symmetric heavy-tailed distributions capable of accommodating outliers and/or influential observations in a better way than the normal distribution. We achieve a fully Bayesian inference using pth-degree spline smooth functions to approximate the nonparametric functions. The likelihood function is utilized to compute not only some Bayesian model selection measures but also to develop Bayesian case-deletion influence diagnostics based on the q-divergence measures. The newly developed procedures are illustrated with an application and simulated data. (C) 2013 Elsevier B.V. All rights reserved.
Perturbation of Numerical Confidential Data via Skew-t Distributions
(INFORMS, 2010) Lee, Seokho; Genton, Marc G.; Arellano Valle, Reinaldo B.
We propose a new data perturbation method for numerical database security problems based on skew-t distributions. Unlike the normal distribution, the more general class of skew-t distributions is a flexible parametric multivariate family that can model skewness and heavy tails in the data. Because databases having a normal distribution are seldom encountered in practice, the newly proposed approach, coined the skew-t data perturbation (STDP) method, is of great interest for database managers. We also discuss how to preserve the sample mean vector and sample covariance matrix exactly for any data perturbation method. We investigate the performance of the STDP method by means of a Monte Carlo simulation study and compare it with other existing perturbation methods. Of particular importance is the ability of STDP to reproduce characteristics of the joint tails of the distribution in order for database users to answer higher-level questions. We apply the STDP method to a medical database related to breast cancer.
Shape mixtures of multivariate skew-normal distributions
(ELSEVIER INC, 2009) Arellano Valle, Reinaldo B.; Genton, Marc G.; Loschi, Rosangela H.
Classes of shape mixtures of independent and dependent multivariate skew-normal distributions are considered and some of their main properties are studied. If interpreted from a Bayesian point of view, the results obtained in this paper bring tractability to the problem of inference for the shape parameter, that is, the posterior distribution can be written in analytic form. Robust inference for location and scale parameters is also obtained under particular conditions. (C) 2008 Elsevier Inc. All rights reserved.
Test procedures based on combination of Bayesian evidences for H-0
(BRAZILIAN STATISTICAL ASSOCIATION, 2012) Loschi, Rosangela H.; Santos, Cristiano C.; Arellano Valle, Reinaldo B.
We introduce two procedures for testing which are based on pooling the posterior evidence for the null hypothesis provided by the full Bayesian significance test and the posterior probability for the null hypothesis. Although the proposed procedures can be used in more general situations, we focus attention in tests for a precise null hypothesis. We prove that the proposed procedure based on the linear operator is a Bayes rule. We also verify that it does not lead to the Jeffreys Lindley paradox. For a precise null hypothesis, we prove that the procedure based on the logarithmic operator is a generalization of Jeffreys test. We apply the results to some well-known probability families. The empirical results show that the proposed procedures present good performances. As a by-product we obtain tests for normality under the skew-normal one.
The centred parametrization for the multivariate skew-normal distribution
(ELSEVIER INC, 2008) Arellano Valle, Reinaldo B.; Azzalini, Adelchi
For statistical inference connected to the scalar skew-normal distribution, it is known that the so-called centred parametrization provides a more convenient parametrization than the one commonly employed for writing the density function. We extend the definition of the centred parametrization to the multivariate case, and study the corresponding information matrix. (C) 2008 Elsevier Inc. All rights reserved.

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