AFFINE INVARIANT MULTIVARIATE RANK-TESTS FOR SEVERAL SAMPLES

Affine invariant analogues of the two-sample Mann-Whitney-Wilcoxon ran k sum test and the c-sample Kruskal-Wallis test for the multivariate l ocation model are introduced. The definition of a multivariate (center ed) rank function in the development is based on the Oja criterion fun ction. This work extends bivariate rank methods discussed by Brown and Hettmansperger (1987a,b) and multivariate sign methods by Hettmansper ger and Oja (1994). The asymptotic distribution theory is developed to consider the Pitman asymptotic efficiencies and the theory is illustr ated by an example.