多元分布和特征值分布的香农熵排序

The Ordering of Shannon Entropies for the Multivariate Distributions and Distributions of Eigenvalues.

作者信息

Tsai Ming-Tien, Hsu Feng-Ju, Tsai Chia-Hsuan

机构信息

Institute of Statistical Science, Academia Sinica, Taipei 11529, Taiwan.

Center for General Education, Saint Mary's Junior College of Medicine, Nursing and Management, Yi-Lang 266, Taiwan.

出版信息

Entropy (Basel). 2019 Feb 20;21(2):201. doi: 10.3390/e21020201.

DOI:10.3390/e21020201

PMID:33266916

原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7514683/

Abstract

In this paper, we prove the Shannon entropy inequalities for the multivariate distributions via the notion of convex ordering of two multivariate distributions. We further characterize the multivariate totally positive of order 2 ( M T P 2 ) property of the distribution functions of eigenvalues of both central Wishart and central MANOVA models, and of both noncentral Wishart and noncentral MANOVA models under the general population covariance matrix set-up. These results can be directly applied to both the comparisons of two Shannon entropy measures and the power monotonicity problem for the MANOVA problem.

摘要

在本文中，我们通过两个多元分布的凸序概念证明了多元分布的香农熵不等式。我们进一步刻画了中心威沙特和中心多元方差分析模型，以及在一般总体协方差矩阵设定下非中心威沙特和非中心多元方差分析模型的特征值分布函数的二元完全正性（MTP2）性质。这些结果可直接应用于两个香农熵测度的比较以及多元方差分析问题的功效单调性问题。