Wishart and pseudo-Wishart distributions and some applications to shape theory

被引：62

作者：

DiazGarcia, JA ^{[1
]}

Jaimez, RG ^{[1
]}

Mardia, KV ^{[1
]}

机构：

[1] UNIV LEEDS,LEEDS LS2 9JT,W YORKSHIRE,ENGLAND

来源：

JOURNAL OF MULTIVARIATE ANALYSIS | 1997年 / 63卷 / 01期

关键词：

singular matrix distributions; Wishart distribution; Pseudo-Wishart distribution; Normal matrix variate distribution; Noncentral distributions; singular values; Stiefel manifold; shape; size-and-shape;

D O I：

10.1006/jmva.1997.1689

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Suppose that X similar to N-N x m(mu, Sigma, Theta). An expression for the density function is given when Sigma greater than or equal to 0 and/or Theta greater than or equal to 0. An extension of Uhlig's result (Uhlig [17]) is expanded for the singular value decomposition of a matrix Z of order N x m when the rank (Z) = q less than or equal to min(N, m). This paper fills an important gap in unifying, for the first time, all Wishart and pseudo-Wishart distributions, whether central or noncentral, whether singular or nonsingular, and applying them in shape analysis. In particular, the shape density and the size-and-shape cone density are obtained for the singular general case. (C) 1997 Academic Press.

引用

页码：73 / 87

页数：15