Adaptive Nonparametric Tests for the Generalized Behrens-Fisher Problem

Abstract

Some adaptive test procedures are developed for the generalized Behrens-Fisher problem. The one having a deterministic approach is based on calculating a measure of symmetry from each sample and using them as a basis for choosing between the modifiedWilcoxon-Mann-Whitney test (Fligner and Policello, 1981) and the modified Mood’s median test (Fligner and Rust, 1982). The other one is a probabilistic approach which also uses a combination of the modified Wilcoxon-Mann-Whitney test and the modified Mood’smedian test according to an evidence of asymmetry provided by the p-value from the triples test for symmetry given in Randles, Fligner, Policello, and Wolfe (1980). This probabilistic approach is further modified by using a suitable function of the p-value from the triples test. A simulation study reveals that the modified procedure performs reasonably well in terms of power and attainment of the nominal size.