Open Access
May 2017 CLT for eigenvalue statistics of large-dimensional general Fisher matrices with applications
Shurong Zheng, Zhidong Bai, Jianfeng Yao
Bernoulli 23(2): 1130-1178 (May 2017). DOI: 10.3150/15-BEJ772


Random Fisher matrices arise naturally in multivariate statistical analysis and understanding the properties of its eigenvalues is of primary importance for many hypothesis testing problems like testing the equality between two covariance matrices, or testing the independence between sub-groups of a multivariate random vector. Most of the existing work on random Fisher matrices deals with a particular situation where the population covariance matrices are equal. In this paper, we consider general Fisher matrices with arbitrary population covariance matrices and develop their spectral properties when the dimensions are proportionally large compared to the sample size. The paper has two main contributions: first the limiting distribution of the eigenvalues of a general Fisher matrix is found and second, a central limit theorem is established for a wide class of functionals of these eigenvalues. Applications of the main results are also developed for testing hypotheses on high-dimensional covariance matrices.


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Shurong Zheng. Zhidong Bai. Jianfeng Yao. "CLT for eigenvalue statistics of large-dimensional general Fisher matrices with applications." Bernoulli 23 (2) 1130 - 1178, May 2017.


Received: 1 September 2014; Revised: 1 April 2015; Published: May 2017
First available in Project Euclid: 4 February 2017

zbMATH: 1375.60066
MathSciNet: MR3606762
Digital Object Identifier: 10.3150/15-BEJ772

Keywords: central limit theorem , equality of covariance matrices , large-dimensional covariance matrices , large-dimensional Fisher matrix , Linear spectral statistics

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

Vol.23 • No. 2 • May 2017
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