Title

Some tests for the equality of covariance matrices

Authors

Authors

J. R. Schott

Abbreviated Journal Title

J. Stat. Plan. Infer.

Keywords

elliptical distribution; kurtosis; Wald statistic; VARIANCE; ROBUST; Statistics & Probability

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. (C) 2001 Elsevier Science B.V. All rights reserved.

Journal Title

Journal of Statistical Planning and Inference

Volume

94

Issue/Number

1

Publication Date

1-1-2001

Document Type

Article

Language

English

First Page

25

Last Page

36

WOS Identifier

WOS:000167188800003

ISSN

0378-3758

Share

COinS