Expressing the largest eigenvalue of a singular beta F-matrix with heterogeneous hypergeometric functions

Autor:	Shimizu, Koki, Hashiguchi, Hiroki
Rok vydání:	2020
Předmět:	Mathematics - Statistics Theory
Druh dokumentu:	Working Paper
Popis:	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. Comment: 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")
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2004.09833 Zobrazit plný text záznamu View this record from Arxiv