Dispersive comparison of distributions: a multisample testing problem

A k-sample testing problem for the dispersive comparison of distributions in the fully nonparametric sense of Bickel and Lehmann (1979) and Lewis and Thompson (1981) is considered. A functional which is monotone with respect to the ordering in dispersion is proposed. Asymptotic laws of the resulting test statistics are established. The tests are shown to be asymptotically distribution free and consistent. A result concerning the optimality in this class of tests, under a sequence of local alternatives, is obtained and asymptotic relative efficiencies with respect to other tests for some specific alternatives are given.Nonparametric Dispersive ordering k-sample scale problem Test for dispersion Order statistic Invariance