Multivariate extended skew-t distributions and related families

Handle URI:
http://hdl.handle.net/10754/598921
Title:
Multivariate extended skew-t distributions and related families
Authors:
Arellano-Valle, Reinaldo B.; Genton, Marc G.
Abstract:
A 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.
Citation:
Arellano-Valle RB, Genton MG (2010) Multivariate extended skew-t distributions and related families. METRON 68: 201–234. Available: http://dx.doi.org/10.1007/BF03263536.
Publisher:
Springer Nature
Journal:
METRON
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
Dec-2010
DOI:
10.1007/BF03263536
Type:
Article
ISSN:
0026-1424; 2281-695X
Sponsors:
The first author was partially supported by grant FONDECYT 1085241-Chile. The second authorwas partially supported by NSF grants DMS-0504896, CMG ATM-0620624, and by Award No.KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorArellano-Valle, Reinaldo B.en
dc.contributor.authorGenton, Marc G.en
dc.date.accessioned2016-02-25T13:43:45Zen
dc.date.available2016-02-25T13:43:45Zen
dc.date.issued2010-12en
dc.identifier.citationArellano-Valle RB, Genton MG (2010) Multivariate extended skew-t distributions and related families. METRON 68: 201–234. Available: http://dx.doi.org/10.1007/BF03263536.en
dc.identifier.issn0026-1424en
dc.identifier.issn2281-695Xen
dc.identifier.doi10.1007/BF03263536en
dc.identifier.urihttp://hdl.handle.net/10754/598921en
dc.description.abstractA 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.en
dc.description.sponsorshipThe first author was partially supported by grant FONDECYT 1085241-Chile. The second authorwas partially supported by NSF grants DMS-0504896, CMG ATM-0620624, and by Award No.KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherSpringer Natureen
dc.titleMultivariate extended skew-t distributions and related familiesen
dc.typeArticleen
dc.identifier.journalMETRONen
dc.contributor.institutionDepartamento de Estadística Facultad de Matemática Pontificia, Universidad Católica de Chile, Santiago 22, Chileen
dc.contributor.institutionDepartment of Statistics, Texas A&M University, College Station, TX, 77843-3143, USAen
kaust.grant.numberKUS-C1-016-04en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.