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The exact distribution of the largest eigenvalue of a singular beta F-matrix for Roy's test

21 April 2020
Koki Shimizu
Hiroki Hashiguchi
ArXiv (abs)PDFHTML
Abstract

In this paper, the exact distribution of the largest eigenvalue of a singular random matrix for Roy's test 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 function of eigenvalues and the exact distribution of the largest eigenvalue in terms of heterogeneous hypergeometric functions.

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