On the limiting distributions of multivariate depth-based rank sum statistics and related tests

Abstract

A depth-based rank sum statistic for multivariate data introduced by Liu and Singh [J. Amer. Statist. Assoc. 88 (1993) 252--260] as an extension of the Wilcoxon rank sum statistic for univariate data has been used in multivariate rank tests in quality control and in experimental studies. Those applications, however, are based on a conjectured limiting distribution, provided by Liu and Singh [J. Amer. Statist. Assoc. 88 (1993) 252--260]. The present paper proves the conjecture under general regularity conditions and, therefore, validates various applications of the rank sum statistic in the literature. The paper also shows that the corresponding rank sum tests can be more powerful than Hotelling's T^2 test and some commonly used multivariate rank tests in detecting location-scale changes in multivariate distributions.

Published at http://dx.doi.org/10.1214/009053606000000876 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Cited by in corpus (13)

• Nonparametric multivariate rank tests and their unbiasedness
• Data depth and floating body
• Quadratic distances on probabilities: A unified foundation
• DepthProc An R Package for Robust Exploration of Multidimensional Economic Phenomena
• Fully distribution-free center-outward rank tests for multiple-output regression and MANOVA
• Center-Outward Distribution Functions, Quantiles, Ranks, and Signs in ${\mathbb{R}}^d$
• Two Procedures for Robust Monitoring of Probability Distributions of Economic Data Streams induced by Depth Functions
• Evaluating proxy influence in assimilated paleoclimate reconstructions -- Testing the exchangeability of two ensembles of spatial processes
• Are Made and Missed Different? An analysis of Field Goal Attempts of Professional Basketball Players via Depth Based Testing Procedure
• A note on the Regularity of Center-Outward Distribution and Quantile Functions
• On Weighted Multivariate Sign Functions
• Symmetrisation of a class of two-sample tests by mutually considering depth ranks including functional spaces
• Distribution-free tests of multivariate independence based on center-outward quadrant, Spearman, Kendall, and van der Waerden statistics