Assessing the similarity of distributions - finite sample performance of the empirical mallows distance

Abstract

The problem of assessing similarity of two cumulative distribution functions (c.d.f.'s) has been the topic of a previous paper by the authors (Munk and Czado (1995)). Here, we developed an asymptotic test based on a trimmed version of the Mallows distance (Mallows 1972) between two c.d.f.'s F and G. This allows to assess the similarity of two c.d.f.'s with respect to this distance at controlled type I error rate. In particular, this applies to bioequivalence testing within a purely nonparametric setting. In this paper, we investigate the finite sample behavior of this test. The effect of trimming and non equal sample size on the observed power and level is studied. Sample size driven recommendations for the choice of the trimming bounds are given in order to minimize the bias. Finally, assuming normality and homogeneous variances, we simulate the relative efficiency of the Mallows test to the (asymptotically optimal) standard equivalence t test, which reveals the Mallows test as a robust alternative to the standard equivalence t test.