Multivariate extended skew-t distributions and related families

被引：69

作者：

Arellano-Valle R.B. ^{[1
,2
]}

Genton M.G. ^{[1
,2
]}

机构：

[1] Departamento de Estadística, Facultad de Matemática, Pontificia Universidad Católica de Chile

[2] Department of Statistics Texas, A and M University, College Station

来源：

METRON | 2010年 / 68卷 / 3期

基金：

美国国家科学基金会;

关键词：

Confidential data perturbation; Elliptically contoured distributions; Fisher information; Kurtosis; Non-normal; Skewness;

D O I：

10.1007/BF03263536

中图分类号：

学科分类号：

摘要：

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.

引用

页码：201 / 234

页数：33

共 30 条

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