Abstract: It is well known that in a general multi-parameter setting, there may not exist any unique best test. More importantly, unlike the univariate case, the power of different test procedures could vary remarkably. In this article we extend results of Hsu (1945) and introduce a new class of tests that have best average power for multivariate linear hypotheses. A simple method to implement the new tests is also provided.
Key words and phrases: Average power, multivariate linear hypotheses, multivariate location problem, Fisher's method of combining tests, U distribution.