Type
ArticleKAUST Grant Number
KUS-C1-016-04Date
2012-12-22Online Publication Date
2012-12-22Print Publication Date
2010-12Permanent link to this record
http://hdl.handle.net/10754/598921
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Show full item recordAbstract
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.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).Publisher
Springer NatureJournal
METRONae974a485f413a2113503eed53cd6c53
10.1007/BF03263536