A Convex Combination of Two-Sample U-Statistics

Abstract

A convex combination of one-sample U-statistics was introduced by Toda and Yamato (2001) and its Edgeworth expansion was derived by Yamato et al. (2003). We introduce a convex combination of two-sample U-statistics, which includes two-sample U-statistic, V-statistic and limit of Bayes estimate. Its Edgeworth expansion is derived with remainder term o(N^−1/2), under the condition that the kernel is non-degenerate. We give some examples of the expansion for three statistics, two-sample U-statistic, V-statistic and limit of Bayes estimate, based on some distributions.