Noncentral matrix quadratic forms of the skew elliptical variables

doi:10.1016/j.jmva.2007.07.003

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	Noncentral matrix quadratic forms of the skew elliptical variables
	Fang, B. Q.
	2008-07-01
发表期刊	JOURNAL OF MULTIVARIATE ANALYSIS
ISSN	0047-259X
卷号	99 期号:6 页码:1105-1127
摘要	In this paper, the noncentral matrix quadratic forms of the skew elliptical variables are studied. A family of the matrix variate noncentral generalized Dirichlet distributions is introduced as the extension of the noncentral Wishart distributions, the Dirichlet distributions and the noncentral generalized Dirichlet distributions. Main distributional properties are investigated. These include probability density and closure property under linear transformation and marginalization, the joint distribution of the sub-matrices of the matrix quadratic forms in the skew elliptical variables and the moment generating functions and Bartlett's decomposition of the matrix quadratic forms in the skew normal variables. Two versions of the noncentral Cochran's Theorem for the matrix variate skew normal distributions are obtained, providing sufficient and necessary conditions for the quadratic forms in the skew normal variables to have the matrix variate noncentral generalized Dirichlet distributions. Applications include the properties of the least squares estimation in multivariate linear model and the robustness property of the Wilk's likelihood ratio statistic in the family of the matrix variate skew elliptical distributions. (C) 2007 Elsevier Inc. All rights reserved.
关键词	normal distribution skew normal distribution skew elliptical distribution quadratic forms Cochran's Theorem
DOI	10.1016/j.jmva.2007.07.003
语种	英语
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000256804400006
出版者	ELSEVIER INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/6028
专题	中国科学院数学与系统科学研究院
通讯作者	Fang, B. Q.
作者单位	Chinese Acad Sci, Inst Appl Math, Acad Math & Syst & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Fang, B. Q.. Noncentral matrix quadratic forms of the skew elliptical variables[J]. JOURNAL OF MULTIVARIATE ANALYSIS,2008,99(6):1105-1127.
APA	Fang, B. Q..(2008).Noncentral matrix quadratic forms of the skew elliptical variables.JOURNAL OF MULTIVARIATE ANALYSIS,99(6),1105-1127.
MLA	Fang, B. Q.."Noncentral matrix quadratic forms of the skew elliptical variables".JOURNAL OF MULTIVARIATE ANALYSIS 99.6(2008):1105-1127.