Testing Significance of a Mean Vector - A Possible Alternative to Hotelling's T Squared.

摘要

In problems involving multivariate measurements experimental considerations often indicate grouping of variables into subsets ordered according to their importance. In such situations, the problems such as comparison of two mean vectors and profile analysis may be treated by Hotelling's T-square-test, adapted along the lines of the step-wise procedure of J. Roy, or the well known test for additional information due to Rao. In this paper, a modification of the step-wise procedure obtained by combining the component tests is studied. The exact Bahadur slopes of resulting procedures are computed and it is shown that the procedure based upon Fisher's combination method is asymptotically equivalent to Hotelling's T-square. A Monte Carlo study suggests that even in small samples the power functions of the new method and Hotelling's T-square-test are practically equivalent.