Reinaldo B. Arellano-Valle
Pontifical Catholic University of Chile
Network
Latest external collaboration on country level. Dive into details by clicking on the dots.
Publication
Featured researches published by Reinaldo B. Arellano-Valle.
Journal of data science | 2005
Reinaldo B. Arellano-Valle; Heleno Bolfarine; Victor H. Lachos
Normality (symmetric) of the random effects and the within-subject errors is a routine assumptions for the linear mixed model, but it may be unrealistic, obscuring important features of among- and within-subjects variation. We relax this assumption by considering that the random effects and model errors follow a skew-normal distributions, which includes normality as a special case and provides flexibility in capturing a broad range of non-normal behavior. The marginal distribution for the observed quantity is derived which is expressed in closed form, so inference may be carried out using existing statistical software and standard optimization techniques. We also implement an EM type algorithm which seem to provide some advantages over a direct maximization of the likelihood. Results of simulation studies and applications to real data sets are reported.
Communications in Statistics-theory and Methods | 2004
Reinaldo B. Arellano-Valle; Héctor W. Gómez; Fernando A. Quintana
Abstract We introduce a new family of asymmetric normal distributions that contains Azzalinis skew-normal (SN) distribution as a special case. We study the main properties of this new family, showing in particular that it may be generated via mixtures on the SN asymmetry parameter when the mixing distribution is normal. This property provides a Bayesian interpretation of the new family.
Journal of Applied Statistics | 2007
Reinaldo B. Arellano-Valle; Heleno Bolfarine; Victor H. Lachos
Linear mixed models (LMM) are frequently used to analyze repeated measures data, because they are more flexible to modelling the correlation within-subject, often present in this type of data. The most popular LMM for continuous responses assumes that both the random effects and the within-subjects errors are normally distributed, which can be an unrealistic assumption, obscuring important features of the variations present within and among the units (or groups). This work presents skew-normal liner mixed models (SNLMM) that relax the normality assumption by using a multivariate skew-normal distribution, which includes the normal ones as a special case and provides robust estimation in mixed models. The MCMC scheme is derived and the results of a simulation study are provided demonstrating that standard information criteria may be used to detect departures from normality. The procedures are illustrated using a real data set from a cholesterol study.
Statistics & Probability Letters | 2002
Reinaldo B. Arellano-Valle; G. del Pino; E. San Martı́n
The univariate and multivariate skew-normal distributions have a number of intriguing properties. It is shown here that these hold for a general class of distributions, defined in terms of independence conditions on signs and absolute values. For this class, two stochastic representations become equivalent, one using conditioning on the positivity of a random vector and the other employing a vector of absolute values. General methods for computing moments and for obtaining the density function of a general skew-distribution are given. The case of spherical and elliptical distributions is briefly discussed.
Communications in Statistics-theory and Methods | 2007
Victor H. Lachos; Heleno Bolfarine; Reinaldo B. Arellano-Valle; Lourdes C. Montenegro
In this article, we present EM algorithms for performing maximum likelihood estimation for three multivariate skew-normal regression models of considerable practical interest. We also consider the restricted estimation of the parameters of certain important special cases of two models. The methodology developed is applied in the analysis of longitudinal data on dental plaque and cholesterol levels.
Metron-International Journal of Statistics | 2010
Reinaldo B. Arellano-Valle; Marc G. Genton
SummaryA class of multivariate extended skew-t (EST) distributions is introduced and studied in detail, along with closely related families such as the subclass of extended skew-normal distributions. Besides mathematical tractability and modeling flexibility in terms of both skewness and heavier tails than the normal distribution, the most relevant properties of the EST distribution include closure under conditioning and ability to model lighter tails as well. The first part of the present paper examines probabilistic properties of the EST distribution, such as various stochastic representations, marginal and conditional distributions, linear transformations, moments and in particular Mardia’s measures of multivariate skewness and kurtosis. The second part of the paper studies statistical properties of the EST distribution, such as likelihood inference, behavior of the profile log-likelihood, the score vector and the Fisher information matrix. Especially, unlike the extended skew-normal distribution, the Fisher information matrix of the univariate EST distribution is shown to be non-singular when the skewness is set to zero. Finally, a numerical application of the conditional EST distribution is presented in the context of confidential data perturbation.
Computational Statistics & Data Analysis | 2013
Jorge I. Figueroa-Zúñiga; Reinaldo B. Arellano-Valle; Silvia L. P. Ferrari
This paper builds on recent research that focuses on regression modeling of continuous bounded data, such as proportions measured on a continuous scale. Specifically, it deals with beta regression models with mixed effects from a Bayesian approach. We use a suitable parameterization of the beta law in terms of its mean and a precision parameter, and allow both parameters to be modeled through regression structures that may involve fixed and random effects. Specification of prior distributions is discussed, computational implementation via Gibbs sampling is provided, and illustrative examples are presented.
Entropy | 2012
Javier E. Contreras-Reyes; Reinaldo B. Arellano-Valle
The aim of this work is to provide the tools to compute the well-known Kullback–Leibler divergence measure for the flexible family of multivariate skew-normal distributions. In particular, we use the Jeffreys divergence measure to compare the multivariate normal distribution with the skew-multivariate normal distribution, showing that this is equivalent to comparing univariate versions of these distributions. Finally, we applied our results on a seismological catalogue data set related to the 2010 Maule earthquake. Specifically, we compare the distributions of the local magnitudes of the regions formed by the aftershocks.
Bayesian Analysis | 2008
Reinaldo B. Arellano-Valle; Luis M. Castro; Marc G. Genton; Héctor W. Gómez
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 re- gression models under some special prior specications 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 hierar- chical 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.
Statistical Methods and Applications | 2012
Reinaldo B. Arellano-Valle; Luis M. Castro; Graciela González-Farías; Karla A. Muñoz-Gajardo
In statistical analysis, particularly in econometrics, it is usual to consider regression models where the dependent variable is censored (limited). In particular, a censoring scheme to the left of zero is considered here. In this article, an extension of the classical normal censored model is developed by considering independent disturbances with identical Student-t distribution. In the context of maximum likelihood estimation, an expression for the expected information matrix is provided, and an efficient EM-type algorithm for the estimation of the model parameters is developed. In order to know what type of variables affect the income of housewives, the results and methods are applied to a real data set. A brief review on the normal censored regression model or Tobit model is also presented.