Scale and shape mixtures of multivariate skew-normal distributions
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Online Publication Date2018-02-26
Print Publication Date2018-07
Permanent link to this recordhttp://hdl.handle.net/10754/627215
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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
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