Scale and shape mixtures of multivariate skew-normal distributions
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
MetadataShow full item record
AbstractWe introduce a broad and flexible class of multivariate distributions obtained by both scale and shape mixtures of multivariate skew-normal distributions. We present the probabilistic properties of this family of distributions in detail and lay down the theoretical foundations for subsequent inference with this model. In particular, we study linear transformations, marginal distributions, selection representations, stochastic representations and hierarchical representations. We also describe an EM-type algorithm for maximum likelihood estimation of the parameters of the model and demonstrate its implementation on a wind dataset. Our family of multivariate distributions unifies and extends many existing models of the literature that can be seen as submodels of our proposal.
CitationArellano-Valle RB, Ferreira CS, Genton MG (2018) Scale and shape mixtures of multivariate skew-normal distributions. Journal of Multivariate Analysis. Available: http://dx.doi.org/10.1016/j.jmva.2018.02.007.
SponsorsThis research was supported by Fondecyt (Chile)1120121 and 1150325, and by the King Abdullah University of Science and Technology (KAUST) . We thank the Editor, Associate Editor and four anonymous reviewers for comments that improved the paper. We also thank Prof. Adelchi Azzalini for suggesting Proposition 1 during a seminar presentation of this work at the University of Padova and Prof. Mauricio Castro for some initial discussions on the topic of this paper.
JournalJournal of Multivariate Analysis
Showing items related by title, author, creator and subject.
Characteristic functions of scale mixtures of multivariate skew-normal distributionsKim, Hyoung-Moon; Genton, Marc G. (Elsevier BV, 2011-08)We obtain the characteristic function of scale mixtures of skew-normal distributions both in the univariate and multivariate cases. The derivation uses the simple stochastic relationship between skew-normal distributions and scale mixtures of skew-normal distributions. In particular, we describe the characteristic function of skew-normal, skew-t, and other related distributions. © 2011 Elsevier Inc.
Extreme-value limit of the convolution of exponential and multivariate normal distributions: Link to the Hüsler–Reiß distributionKrupskii, Pavel; Joe, Harry; Lee, David; Genton, Marc G. (Elsevier BV, 2017-11-02)The multivariate Hüsler–Reiß copula is obtained as a direct extreme-value limit from the convolution of a multivariate normal random vector and an exponential random variable multiplied by a vector of constants. It is shown how the set of Hüsler–Reiß parameters can be mapped to the parameters of this convolution model. Assuming there are no singular components in the Hüsler–Reiß copula, the convolution model leads to exact and approximate simulation methods. An application of simulation is to check if the Hüsler–Reiß copula with different parsimonious dependence structures provides adequate fit to some data consisting of multivariate extremes.
A Monte Carlo Metropolis-Hastings Algorithm for Sampling from Distributions with Intractable Normalizing ConstantsLiang, Faming; Jin, Ick-Hoon (MIT Press - Journals, 2013-08)Simulating from distributions with intractable normalizing constants has been a long-standing problem inmachine learning. In this letter, we propose a new algorithm, the Monte Carlo Metropolis-Hastings (MCMH) algorithm, for tackling this problem. The MCMH algorithm is a Monte Carlo version of the Metropolis-Hastings algorithm. It replaces the unknown normalizing constant ratio by a Monte Carlo estimate in simulations, while still converges, as shown in the letter, to the desired target distribution under mild conditions. The MCMH algorithm is illustrated with spatial autologistic models and exponential random graph models. Unlike other auxiliary variable Markov chain Monte Carlo (MCMC) algorithms, such as the Møller and exchange algorithms, the MCMH algorithm avoids the requirement for perfect sampling, and thus can be applied to many statistical models for which perfect sampling is not available or very expensive. TheMCMHalgorithm can also be applied to Bayesian inference for random effect models and missing data problems that involve simulations from a distribution with intractable integrals. © 2013 Massachusetts Institute of Technology.