Distance testing for selecting the best population

Abstract

We consider testing the null hypothesis that a given population has location parameter greater than or equal to the largest location parameter of k competing populations. We generalize tests proposed by Gupta and Bartholomew by considering tests based on p-distances from the parameter estimate to the null parameter space. It is shown that all tests are equivalent when k→∞ for a class of distributions that includes the normal and uniform distribution. Moreover, we propose the use of adaptive quantiles. Under suitable assumptions the resulting tests are asymptotically equivalent to the uniformly most powerful test for the case that the location parameters of all but one of the populations are known. The increase in power obtained by using adaptive tests is confirmed by a simulation study.