Some tests for the equality of covariance matrices
Abbreviated Journal Title
J. Stat. Plan. Infer.
elliptical distribution; kurtosis; Wald statistic; VARIANCE; ROBUST; Statistics & Probability
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 of Statistical Planning and Inference
"Some tests for the equality of covariance matrices" (2001). Faculty Bibliography 2000s. 8204.