Title

A High-Dimensional Test For The Equality Of The Smallest Eigenvalues Of A Covariance Matrix

Keywords

Principal components analysis; Sums of eigenvalues

Abstract

For the test of sphericity, Ledoit and Wolf [Ann. Statist. 30 (2002) 1081-1102] proposed a statistic which is robust against high dimensionality. In this paper, we consider a natural generalization of their statistic for the test that the smallest eigenvalues of a covariance matrix are equal. Some inequalities are obtained for sums of eigenvalues and sums of squared eigenvalues. These bounds permit us to obtain the asymptotic null distribution of our statistic, as the dimensionality and sample size go to infinity together, by using distributional results obtained by Ledoit and Wolf [Ann. Statist. 30 (2002) 1081-1102]. Some empirical results comparing our test with the likelihood ratio test are also given. © 2005 Elsevier Inc. All rights reserved.

Publication Date

4-1-2006

Publication Title

Journal of Multivariate Analysis

Volume

97

Issue

4

Number of Pages

827-843

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jmva.2005.05.003

Socpus ID

27944490752 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/27944490752

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