Modified Wilcoxon-Mann-Whitney tests of stochastic dominance

Abstract

Given independent samples from two univariate distributions, the one-sided Wilcoxon-Mann-Whitney statistic may be used to conduct a rank-based test of first-order stochastic dominance. We broaden the scope of applicability of such tests by showing that the bootstrap may be used to conduct valid inference in a matched pairs sampling framework permitting dependence between the two samples. Further, we show that a modified bootstrap incorporating an implicit estimate of a contact set may be used to improve power. Numerical simulations indicate that the modified bootstrap effectively controls the null rejection frequencies and delivers improved power, particularly in settings where there is strong dependence between matched pairs. We provide a brief empirical illustration involving Canadian family income data.