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

    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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