The Sampling Distribution of the Total Correlation for Multivariate Gaussian Random Variables

被引：2

作者：

Rowe, Taylor ^{[1
]}

Day, Troy ^{[1
]}

机构：

[1] Queens Univ, Dept Math & Stat, Kingston, ON K7L 3N6, Canada

来源：

ENTROPY | 2019年 / 21卷 / 10期

基金：

加拿大自然科学与工程研究理事会;

关键词：

mutual information; total correlation; multiinformation; sampling distribution; central limit theorem; multivariate mutual information; INFORMATION; ENTROPY;

D O I：

10.3390/e21100921

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The sampling distribution of the total correlation (TC) for a d-dimensional standardized multivariate Gaussian random variable with an identity covariance matrix is derived. It is shown to be the distribution of a sum of generalized beta random variables. It is also shown that, for large dimension and sample size, a central limit theorem holds, providing a Gaussian approximation to the sampling distribution for high dimensional data.

引用

页数：8

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