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On Distribution-Free Tests for the Multivariate Two-Sample Location-Scale Model

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  • Rousson, Valentin

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.

Suggested Citation

  • Rousson, Valentin, 2002. "On Distribution-Free Tests for the Multivariate Two-Sample Location-Scale Model," Journal of Multivariate Analysis, Elsevier, vol. 80(1), pages 43-57, January.
    • Handle: RePEc:eee:jmvana:v:80:y:2002:i:1:p:43-57
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    References listed on IDEAS

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    1. Oja, Hannu, 1983. "Descriptive statistics for multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 1(6), pages 327-332, October.
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    Cited by:

    1. Caiya Zhang & Zhengyan Lin & Jianjun Wu, 2009. "Nonparametric tests for the general multivariate multi-sample problem," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(7), pages 877-888.
    2. Shin-ichi Tsukada, 2019. "High dimensional two-sample test based on the inter-point distance," Computational Statistics, Springer, vol. 34(2), pages 599-615, June.
    3. Biswas, Munmun & Ghosh, Anil K., 2014. "A nonparametric two-sample test applicable to high dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 160-171.
    4. Anil K. Ghosh & Munmun Biswas, 2016. "Distribution-free high-dimensional two-sample tests based on discriminating hyperplanes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 525-547, September.
    5. Sakineh Dehghan & Mohammad Reza Faridrohani, 2019. "Affine invariant depth-based tests for the multivariate one-sample location problem," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 671-693, September.
    6. Petrie, Adam, 2016. "Graph-theoretic multisample tests of equality in distribution for high dimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 145-158.

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