Title

Some Tests For The Equality Of Covariance Matrices

Keywords

62H15; Elliptical distribution; Kurtosis; Wald statistic

Abstract

A Wald statistic, which is asymptotically equivalent to the likelihood ratio criterion, is obtained for the test of the equality of covariance matrices. A more general Wald statistic is constructed under the assumption of elliptical distributions, and the comparison of these two statistics sheds some light on the asymptotic performance of the likelihood ratio test. In particular, we find that the likelihood ratio test is liberal for nonnormal elliptical populations with positive kurtosis and conservative for nonnormal elliptical populations with negative kurtosis. Further, the likelihood ratio test cannot be adjusted by a scalar multiple so as to retain its asymptotic chi-squared distribution over the class of elliptical distributions. A Wald test, appropriate for more general populations, is also obtained. © 2001 Elsevier Science B.V.

Publication Date

3-1-2001

Publication Title

Journal of Statistical Planning and Inference

Volume

94

Issue

1

Number of Pages

25-36

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/S0378-3758(00)00209-3

Socpus ID

0042403643 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0042403643

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