Expressing the largest eigenvalue of a singular beta F-matrix with heterogeneous hypergeometric functions
Statistics Theory
2021-03-17 v2 Statistics Theory
Abstract
In this paper, the exact distribution of the largest eigenvalue of a singular random matrix for multivariate analysis of variance (MANOVA) is discussed. The key to developing the distribution theory of eigenvalues of a singular random matrix is to use heterogeneous hypergeometric functions with two matrix arguments. In this study, we define the singular beta F-matrix and extend the distributions of a nonsingular beta F -matrix to the singular case. We also give the joint density of eigenvalues and the exact distribution of the largest eigenvalue in terms of heterogeneous hypergeometric functions.
Keywords
Cite
@article{arxiv.2004.09833,
title = {Expressing the largest eigenvalue of a singular beta F-matrix with heterogeneous hypergeometric functions},
author = {Koki Shimizu and Hiroki Hashiguchi},
journal= {arXiv preprint arXiv:2004.09833},
year = {2021}
}
Comments
The title is changed (the old title is "The exact distribution of the largest eigenvalue of a singular beta F-matrix for Roy's test")