Title

A high-dimensional test for the equality of the smallest eigenvalues of a covariance matrix

Authors

Authors

J. R. Schott

Comments

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Abbreviated Journal Title

J. Multivar. Anal.

Keywords

principal components analysis; sums of eigenvalues; ROOTS; LIMIT; Statistics & Probability

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 LIS 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. (C) 2005 Elsevier Inc. All rights reserved.

Journal Title

Journal of Multivariate Analysis

Volume

97

Issue/Number

4

Publication Date

1-1-2006

Document Type

Article

Language

English

First Page

827

Last Page

843

WOS Identifier

WOS:000236339200003

ISSN

0047-259X

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