On distribution-free tests for the multivariate two-sample location-scale model

Abstract

In this paper, we propose simple exact procedures for testing both a location shift and/or a scale change between two multivariate distributions. Our tests are strictly distribution-free and can be made either scale invariant or rotation invariant. Our approach combines a generalization of the Wilcoxon test based on projections of the data onto the first principal component, a generalization of the Siegel-Tukey test based on the concept of data depth, and a bivariate test for the location problem proposed by K.V. Mardia (1967, J. Roy. Statist. Soc. Ser. B 29, 320-342). In addition, we show that the limiting null distribution of a test statistic proposed by R.Y. Liu and K. Singh (1993, J. Amer. Statist. Assoc. 88, 252-260) does not depend on the depth considered. © 2001 Elsevier Science.