Chi-Square Approximation for the Distribution of Individual Eigenvalues of a Singular Wishart Matrix-Reference-Cited by-同舟云学术

Chi-Square Approximation for the Distribution of Individual Eigenvalues of a Singular Wishart Matrix

Published:2024-03-20 Issue:6 Volume:12 Page:921
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Shimizu Koki¹^ORCID,Hashiguchi Hiroki¹^ORCID

Affiliation:

1. Department of Applied Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan

Abstract

This paper discusses the approximate distributions of eigenvalues of a singular Wishart matrix. We give the approximate joint density of eigenvalues by Laplace approximation for the hypergeometric functions of matrix arguments. Furthermore, we show that the distribution of each eigenvalue can be approximated by the chi-square distribution with varying degrees of freedom when the population eigenvalues are infinitely dispersed. The derived result is applied to testing the equality of eigenvalues in two populations.

Funder

Japan Society for the Promotion of Science

Publisher

MDPI AG

Link

https://www.mdpi.com/2227-7390/12/6/921/pdf

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