A locally most powerful invariant test for the equality of means associated with covariate discriminant analysis

In this paper, the authors propose a locally most powerful invariant test for the equality of means in the presence of covariate variables. Also the null and nonnull distributions associated with the above test are developed. This problem arises in covariate discriminant analysis and has been treated by various authors, notably Cochran and Bliss 1948, Ann. Math. Statist.19, 151–176 and Rao 1949, Sankhyã9 343–366; 1966. The test derived here locally dominates in power the tests proposed so far. It is also shown that the Cochran-Bliss test is uniformly most powerful in the class of conditional invariant tests.