ON SINGULAR WISHART AND SINGULAR MULTIVARIATE BETA-DISTRIBUTIONS
成果类型：
Article
署名作者：
UHLIG, H
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/aos/1176325375
发表日期：
1994
页码：
395-405
关键词：
摘要：
This paper extends the study of Wishart and multivariate beta distributions to the singular case, where the rank is below the dimensionality. The usual conjugacy is extended to this case. A volume element on the space of positive semidefinite m x m matrices of rank n < m is introduced and some transformation properties established. The density function is found for all rank-n Wishart distributions as well as the rank-1 multivariate beta distribution. To do that, the Jacobian for the transformation to the singular value decomposition of general m x n matrices is calculated. The results in this paper are useful in particular for updating a Bayesian posterior when tracking a time-varying variance-covariance matrix.