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Robustness Study of MANOVA Statistics for Profile Analysis and Tests of Dimensionality
by
Solomon W. Harrar
University of Montana
We consider the comparison mean vectors for k groups when k is large and sample size per group is fixed. The asymptotic null and non-null distributions of the normal theory Likelihood Ratio, Lawley-Hotelling and Bartlett-Nanda-Pillai Statistics are studied under general conditions. We extend the results for tests on the profiles of the mean vectors and tests on the dimension of the hyper plane formed by the mean vectors. In all these three MANOVA problems, the asymptotic null and null distributions are normal. Furthermore, both the null and non-null distributions are shown to be asymptotically invariant to non-normality when the group sample sizes are equal. In the unbalanced case, we show that a slight modification of the test statistics will lead to asymptotically robust tests. Numerical results provide strong support for these conclusions.
Date received: February 28, 2007
Copyright © 2007 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 # cata-94.