Singular Wishart and multivariate beta distributions

• 成果类型: Article
• 署名作者: Srivastava, MS
• 署名单位: University of Toronto
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1065705118
• 发表日期: 2003
• 页码: 1537-1560
• 关键词: density-free approach

摘要

In this article, we consider the case when the number of observations n is less than the dimension p of the random vectors which are assumed to be independent and identically distributed as normal with nonsingular covariance matrix. The central and noncentral distributions of the singular Wishart matrix S = XX', where X is the p x n matrix of observations are derived with respect to Lebesgue measure. Properties of this distribution are given. When the covariance matrix is singular, pseudo singular Wishart distribution is also derived. The result is extended to any distribution of the type f (XX') for the central case. Singular multivariate beta distributions with respect to Lebesgue measure are also given.