Limiting Distribution of Two-SampLe Degenerate U-Statistic under Contiguous ALternatives and AppLications

摘要

In this paper, a limiting distribution of a two-sample degenerate U-statistic is obtained under contiguous alternatives. These results are applied to find the limiting distribution of Lehmann's (1951) test statistic for testing the equality of two distributions against general alternatives. Anderson's (1962) statistic is shown to have the same limiting distribution as Lehmann's statistic.