AN EXACT DECOMPOSITION THEOREM AND A UNIFIED VIEW OF SOME RELATED DISTRIBUTIONS FOR A CLASS OF EXPONENTIAL TRANSFORMATION MODELS ON SYMMETRICAL CONES

• 成果类型: Article
• 署名作者: MASSAM, H
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176325374
• 发表日期: 1994
• 页码: 369-394
• 关键词: hyperboloid distribution

摘要

A class of exponential transformation models is defined on symmetric cones OMEGA with the group of automorphisms on OMEGA as the acting group. We show that these models are reproductive and the exponent of their joint distribution for a given sample of size q can be split into q independent components, introducing one sample point at a time. The automorphism group can be factorized into the group of positive dilation and another group. Accordingly, the symmetric cone OMEGA can be seen as the direct product of R+ and a unit orbit, and every x in OMEGA can be identified by its orbital decomposition. We derive the distributions of the independent components of the exponent, of the ''length'' of x, the ''direction'' of x, the conditional distribution of the direction given the length and other distributions for a given sample. The Wishart distribution and the hyperboloid distribution are two special cases in the class we define. We also give a unified view of several distributions which are usually treated separately