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

2020/04/21 by Koki Shimizu, Shimizu, Koki, Hiroki Hashiguchi +1
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #FOS: Mathematics #Random Matrices and Applications #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2004.09833

openalex publication_date 2020/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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