Chi-square approximation for the distribution of individual eigenvalues of a singular Wishart matrix
Statistics Theory
2023-06-09 v1 Statistics Theory
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 hyper-geometric 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
Keywords
Cite
@article{arxiv.2306.05160,
title = {Chi-square approximation for the distribution of individual eigenvalues of a singular Wishart matrix},
author = {Koki Shimizu and Hiroki Hashiguchi},
journal= {arXiv preprint arXiv:2306.05160},
year = {2023}
}