Noncentral matrix quadratic forms of the skew elliptical variables
文献类型：期刊论文
| 作者 | Fang, B. Q. |
| 刊名 | JOURNAL OF MULTIVARIATE ANALYSIS
 |
| 出版日期 | 2008-07-01 |
| 卷号 | 99期号:6页码:1105-1127 |
| 关键词 | normal distribution skew normal distribution skew elliptical distribution quadratic forms Cochran's Theorem |
| ISSN号 | 0047-259X |
| DOI | 10.1016/j.jmva.2007.07.003 |
| 英文摘要 | 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. |
| 语种 | 英语 |
| WOS记录号 | WOS:000256804400006 |
| 出版者 | ELSEVIER INC |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/6027]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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