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

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 a...

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Detalles Bibliográficos
Autores principales: Rowe, Taylor, Day, Troy
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2019
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514253/
http://dx.doi.org/10.3390/e21100921
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author Rowe, Taylor
Day, Troy
author_facet Rowe, Taylor
Day, Troy
author_sort Rowe, Taylor
collection PubMed
description 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.
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spelling pubmed-75142532020-11-09 The Sampling Distribution of the Total Correlation for Multivariate Gaussian Random Variables Rowe, Taylor Day, Troy Entropy (Basel) Article 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. MDPI 2019-09-22 /pmc/articles/PMC7514253/ http://dx.doi.org/10.3390/e21100921 Text en © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Rowe, Taylor
Day, Troy
The Sampling Distribution of the Total Correlation for Multivariate Gaussian Random Variables
title The Sampling Distribution of the Total Correlation for Multivariate Gaussian Random Variables
title_full The Sampling Distribution of the Total Correlation for Multivariate Gaussian Random Variables
title_fullStr The Sampling Distribution of the Total Correlation for Multivariate Gaussian Random Variables
title_full_unstemmed The Sampling Distribution of the Total Correlation for Multivariate Gaussian Random Variables
title_short The Sampling Distribution of the Total Correlation for Multivariate Gaussian Random Variables
title_sort sampling distribution of the total correlation for multivariate gaussian random variables
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514253/
http://dx.doi.org/10.3390/e21100921
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