Browsing by Author "Genton, Marc G."
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- ItemA 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.
- ItemBayesian 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.
- ItemOn 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.
- ItemOn 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.
- ItemPerturbation 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.
- ItemScale and shape mixtures of multivariate skew-normal distributions(2018) Arellano Valle, Reinaldo Boris; Ferreira, Clécio S.; Genton, Marc G.
- ItemShannon entropy and mutual information for multivariate skew-elliptical distributions(2013) Arellano Valle, Reinaldo Boris; Contreras Reyes, Javier E.; Genton, Marc G.
- ItemShape 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.
- ItemSkewed factor models using selection mechanisms(2016) Kim, Hyoung-Moon.; Maadooliat, Mehdi.; Arellano Valle, Reinaldo Boris; Genton, Marc G.