Affine Invariant Rank Methods in the Bivariate Location Model

Abstract

SUMMARY The generalized multivariate median of Oja (Statist. and Prob. Letters 1(1983), 327–332) is used to define a multivariate notion of quantile, or rank, and to define a measure of scatter of multivariate linear models. The latter, when applied to the one- and two-sample bivariate location models, yields affine invariant analogues of the Wilcoxon rank-sum and signed-rank tests, and of the corresponding estimates.