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


Rousson, V (2002). On distribution-free tests for the multivariate two-sample location-scale model. Journal of Multivariate Analysis, 80(1):43-57.

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. B29, 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.

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. B29, 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.

Citations

8 citations in Web of Science®
9 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:data depth; multivariate orderings; nonparametric methods; principal component analysis; rank tests
Language:English
Date:2002
Deposited On:29 Nov 2010 16:27
Last Modified:05 Apr 2016 13:25
Publisher:Elsevier
ISSN:0047-259X
Publisher DOI:https://doi.org/10.1006/jmva.2000.1981
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1010.62035

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