Concentrated matrix Langevin distributions

JOURNAL OF MULTIVARIATE ANALYSIS

卷:85

Article

Chikuse, Y

关键词: Stiefel manifold;    Grassmann manifold;    orthogonal projection matrix;    asymptotics for large concentrations;    matrix Langevin distributions;    hypergeometric functions with matrix arguments;   

DOI  :  10.1016/S0047-259X(02)00065-9

来源: Elsevier

【 摘 要 】

This paper concerns the matrix Langevin distributions, exponential-type distributions defined on the two manifolds of our interest, the Stiefel manifold V-k,V-m and the manifold P-k,P-m-k of m x m orthogonal projection matrices idempotent of rank k which is equivalent to the Grassmann manifold G(k,m-k). Asymptotic theorems are derived when the concentration parameters of the distributions are large. We investigate the asymptotic behavior of distributions of some (matrix) statistics constructed based on the sample mean matrices in connection with testing hypotheses of the orientation parameters, and obtain asymptotic results in the estimation of large concentration parameters and in the classification of the matrix Langevin distributions. (C) 2003 Elsevier Science (USA). All rights reserved.

【 授权许可】

Free