The Lukacs-Olkin-Rubin characterization of Wishart distributions on symmetric cones
成果类型：
Article
署名作者：
Casalis, M; Letac, G
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
发表日期：
1996
页码：
763-786
关键词：
摘要：
We characterize the Wishart distributions on a symmetric cone C. If C = (0, +infinity), this has been done by Lukacs in 1955. If C is the cone of positive definite symmetric matrices, this has been done by Olkin and Rubin in 1962. We both shorten and extend the Olkin-Rubin proof (sometimes obscure) by using three modern ideas: (i) try to avoid artificial coordinates in differential geometry; (ii) the variance function of a natural exponential family F characterizes F; (iii) symmetric matrices are a particular example of a Euclidean simple Jordan algebra.