Scale and shape mixtures of multivariate skew-normal distributions

Reinaldo B. Arellano-Valle; Clécio S. Ferreira; Marc G. Genton

doi:10.1016/j.jmva.2018.02.007

Scale and shape mixtures of multivariate skew-normal distributions

Reinaldo B. Arellano-Valle, Clécio S. Ferreira, Marc G. Genton^*

^*Corresponding author for this work

Computer, Electrical and Mathematical Sciences and Engineering

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

Abstract

We 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.

Original language	English (US)
Pages (from-to)	98-110
Number of pages	13
Journal	Journal of Multivariate Analysis
Volume	166
DOIs	https://doi.org/10.1016/j.jmva.2018.02.007
State	Published - Jul 2018

Bibliographical note

Funding Information:
This research was supported by Fondecyt (Chile) 1120121 and 1150325 , by FAPEMIG (Minas Gerais State Foundation for Research Development) grant CEX APQ 01944/17 , 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.

Publisher Copyright:
© 2018 Elsevier Inc.

Keywords

EM-algorithm
Scale mixtures of normal distributions
Scale mixtures of skew-normal distributions
Shape mixtures of skew-normal distributions
Skew scale mixtures of normal distributions
Skew-normal distribution

ASJC Scopus subject areas

Statistics and Probability
Numerical Analysis
Statistics, Probability and Uncertainty

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10.1016/j.jmva.2018.02.007

Cite this

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title = "Scale and shape mixtures of multivariate skew-normal distributions",

abstract = "We 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.",

keywords = "EM-algorithm, Scale mixtures of normal distributions, Scale mixtures of skew-normal distributions, Shape mixtures of skew-normal distributions, Skew scale mixtures of normal distributions, Skew-normal distribution",

author = "Arellano-Valle, {Reinaldo B.} and Ferreira, {Cl{\'e}cio S.} and Genton, {Marc G.}",

note = "Funding Information: This research was supported by Fondecyt (Chile) 1120121 and 1150325 , by FAPEMIG (Minas Gerais State Foundation for Research Development) grant CEX APQ 01944/17 , 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. Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

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AU - Arellano-Valle, Reinaldo B.

AU - Ferreira, Clécio S.

AU - Genton, Marc G.

N1 - Funding Information: This research was supported by Fondecyt (Chile) 1120121 and 1150325 , by FAPEMIG (Minas Gerais State Foundation for Research Development) grant CEX APQ 01944/17 , 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. Publisher Copyright: © 2018 Elsevier Inc.

PY - 2018/7

Y1 - 2018/7

N2 - We 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.

AB - We 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.

KW - EM-algorithm

KW - Scale mixtures of normal distributions

KW - Scale mixtures of skew-normal distributions

KW - Shape mixtures of skew-normal distributions

KW - Skew scale mixtures of normal distributions

KW - Skew-normal distribution

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DO - 10.1016/j.jmva.2018.02.007

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SN - 0047-259X

VL - 166

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EP - 110

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

ER -

Scale and shape mixtures of multivariate skew-normal distributions

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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