Affine invariant multivariate rank tests for several samples

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