On the Asymptotic Power of a Method for Testing Hypotheses on the Equality of Distributions

In this paper, the asymptotic power of a method for testing hypotheses on the equality of two distributions is investigated; it can be regarded as a generalization of the Wilcoxon-Mann-Whitney test. We consider a class of distributions such that the mathematical expectation of the square of some auxiliary function is finite. For the case where the alternative distribution differs from the zero distribution only by the shift, the asymptotic distribution of the test and the asymptotic power of the test are explicitly found. Up to now, the power of this test has been studied only using statistical modeling.