Some tests for the equality of covariance matrices

    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

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