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December 2016 Approximate eigenvalue distribution for the ratio of Wishart matrices
Shusuke Matsubara, Hiroki Hashiguchi
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SUT J. Math. 52(2): 141-158 (December 2016). DOI: 10.55937/sut/1482245190


We discuss approximations for the distribution of eigenvalues of the ratio of Wishart matrices when the population eigenvalues are infinitely dispersed. The first approximation is expressed as the F distribution with suitable parameters, and the second is expressed by the product of F distributions. Numerical examples show that the proposed approximations are more accurate than the known asymptotic expansions of the normal distribution.

Funding Statement

This research was supported in part by the Japan Society for the Promotion Science, Grant-in-Aid for Scientific Research (C), Nos. 25330033 and 26330053.


The authors would like to thank the editor and the anonymous reviewer for improving this paper.


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Shusuke Matsubara. Hiroki Hashiguchi. "Approximate eigenvalue distribution for the ratio of Wishart matrices." SUT J. Math. 52 (2) 141 - 158, December 2016.


Received: 18 February 2016; Revised: 10 September 2016; Published: December 2016
First available in Project Euclid: 8 June 2022

Digital Object Identifier: 10.55937/sut/1482245190

Primary: 62E20 , 62H10

Keywords: F distribution , hypergeometric function with two matrix arguments , Laplace’s method

Rights: Copyright © 2016 Tokyo University of Science


Vol.52 • No. 2 • December 2016
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