Comparison of powers and exact bahadur slopes of some tests for dimensionality in manova models

In this paper we consider test of dimensionality in MANOVA model. For this testing problem, the likelihood ratio (=LR) test, Lawley-Hotelling (=LH) type test and Bartlett-Nanda-Pillai (=BNP) type test are often used. We obtain the asymptotic expansions of powers of these tests under the local alternatives. Also Bahadur exact slopes of these tests are obtained. Based on these results, we obtain a unified opinion concerning comparison of LR test, LH type test and BNP type test.