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On distribution-free tests for the multivariate two-sample location-scale model. (English) Zbl 1010.62035

Summary: 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 [J. R. Stat. Soc., Ser. B 29, 320-342 (1967; Zbl 0157.48004)]. In addition, we show that the limiting null distribution of a test statistic proposed by R.Y. Liu and K. Singh [J. Am. Stat. Assoc. 88, No. 421, 252-260 (1993; Zbl 0772.62031)] does not depend on the depth considered.

MSC:

62G10 Nonparametric hypothesis testing
62H15 Hypothesis testing in multivariate analysis
62H25 Factor analysis and principal components; correspondence analysis
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