Multivariate multi-sample rank tests for location-scale alternatives

Abstract

A distribution-free test problem for the null hypothesis of equality of multivariate distributions versus location-scale alternatives in a multivariate multi-sample data setting is considered. Asymptotic distributions of random vectors of multivariate linear rank statistics are respectively investigated under the null hypothesis and under a contiguous sequence of the location-scale alternatives and, based on these asymptotic distributions, rank tests which have high asymptotic power are proposed. Each of the proposed test statistics is defined in terms of a sum of multivariate rank test statistics against location alternatives and statistics against scale alternatives, similar to the approach used by Lepage (1971). The limiting distributions are respectively X 2 - and noncentral x 2-distributions under the null hypothesis and under the alternatives. It is shown that the proposed tests are asymptotically power-equivalent to rank tests proposed by shen (1986). Methods of assigning optium scores and the comp...