S. Purkayastha et Ms. Srivastava, ASYMPTOTIC DISTRIBUTIONS OF SOME TEST CRITERIA FOR THE COVARIANCE-MATRIX IN ELLIPTIC DISTRIBUTIONS UNDER LOCAL ALTERNATIVES, Journal of Multivariate Analysis, 55(2), 1995, pp. 165-186
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.