Proof of the conjectures of H.!Uhlig on the singular multivariate beta and the Jacobian of a certain matrix transformation
成果类型：
Article
署名作者：
Díaz-García, JA; Jáimez, RG
署名单位：
University of Granada
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
发表日期：
1997
页码：
2018-2023
关键词：
摘要：
Uhlig proposes two conjectures. The first concerns the Jacobian of the transformation Y = B X B' where B is the matrix m x m and m and X, Y belong to the class of positive semidefinite matrices of the order of m X m of rank n < m, S-m,n(+). The second is concerned with the singular multivariate Beta distribution. This article seeks to prove the two conjectures. The latter result is then extended to the case of the singular multivariate F distribution, and the respective density functions are located for the nonzero positive eigenvalues of the singular Beta and F matrices.