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Asymptotic Expansions of the Distributions of Dempster Test Statistics when the Dimension is Large
by
Tetsuto Himeno
Department of Mathematics, Graduate School of Science, Hiroshima University
In this paper, we obtain the asymptotic expansion of the null distribution of the Dempster's test statistic under a certain linear hypothesis in the MANOVA model when the sample size and the dimension are large. We obtain another asymptotic expansion when the rank of hypothesis is also large. Using these asymptotic expansions, we obtain the Cornish-Fisher expansions of the upper percent points. The errors of these approximations are compared numerically. Next we consider a class of the statistics inculuding the Dempster's test statistic in the case of the two groups without assuming covariance matrices are equal. The limiting powers of the tests in the class are derived, and the optimality is discussed.
Date received: October 14, 2005
Copyright © 2005 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # carm-77.