ASYMPTOTIC DISTRIBUTIONS OF SOME TEST CRITERIA FOR THE COVARIANCE-MATRIX IN ELLIPTIC DISTRIBUTIONS UNDER LOCAL ALTERNATIVES

The asymptotic distributions under local alternatives of two test crit eria for testing the hypothesis that the characteristic roots of the c ovariance matrix of an elliptical population, assumed distinct, are eq ual to a set of specified numbers, are derived. The two tests are the modified likelihood ratio test and a new test criterion proposed in th is context for the normal model. Similar results are given for the two tests for testing that the covariance matrix is a specified positive definite matrix, in which case the two tests are the modified likeliho od ratio test and a test proposed by Rao and Nagao for the normal mode l, and also for a test for the covariance structure in familial data, studied by Srivastava. (C) 1995 Academic Press, Inc.