Depth and a Multivariate Generalization of the Wilcoxon-Mann-Whitney Test

SYNOPTIC ABSTRACT

Tukey's notion of halfspace depth provides, among other things, a new class of location estimators when dealing with multivariate data. Recent advances on how to approximate halfspace depth provide a practical way of employing halfspace in a range of applied problems. The main focus in this paper is on an affine invariant, multivariate generalization of the Wilcoxon-Mann-Whitney test that is based on the halfspace depth of the zero vector relative to the joint distribution of the difference between the marginal distributions. Simulation results on a relevant hypothesis testing method are reported.

Key Words and Phrases:

• halfspace depth
• Tukey's median
• rank-based methods
• affine invariance