两个多元t分布之间的Kullback Leibler距离

数学物理学报 ›› 2005, Vol. 25 ›› Issue (5): 694-709.

两个多元t分布之间的Kullback Leibler距离

白鹏

云南大学统计系云南大学应用统计研究中心昆明

出版日期:2005-10-25 发布日期:2005-10-25
基金资助:
数学天元青年基金和国家自然科学基金（10261009）资助

Kullback Leibler's Divergence between Two Multivariatet Distributions

BAI Peng

Online:2005-10-25 Published:2005-10-25
Supported by:
数学天元青年基金和国家自然科学基金（10261009）资助

摘要/Abstract

摘要：

该文将文［1］的结果推广到多元t分布的情形.结果表明, 两个多元t分布之间的Kullback Leibler距离与分布中的刻度矩阵之比的最大特征根密切相关.作为应用, 文章建立了一种在估计未知正定阵时的熵损失函数.

关键词: 多元t分布, Kullback Leibler距离, 熵损失函数

Abstract:

The paper is devoted to extension of results obtained in paper ［1］to mul tivariate t distributions case. It is shown that the divergence between two mul tivariate t distributions closely depends on the maximum eigenvalue of the rati o of scale matrices in the distributions. As an application, a kind of e ntropy loss function in estimating the unknown positive definite matrix is establis hed.

Key words: Multivariatet distribution, Kullback Leibler divergence, Entropy loss function

中图分类号:

白鹏. 两个多元t分布之间的Kullback Leibler距离[J]. 数学物理学报, 2005, 25(5): 694-709.

BAI Peng. Kullback Leibler's Divergence between Two Multivariatet Distributions[J]. Acta mathematica scientia,Series A, 2005, 25(5): 694-709.