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A Wilcoxon–Mann–Whitney-type test for infinite-dimensional data

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  • Anirvan Chakraborty
  • Probal Chaudhuri

Abstract

The Wilcoxon–Mann–Whitney test is a robust competitor of the $t$ test in the univariate setting. For finite-dimensional multivariate non-Gaussian data, several extensions of the Wilcoxon–Mann–Whitney test have been shown to outperform Hotelling's $T^{2}$ test. In this paper, we study a Wilcoxon–Mann–Whitney-type test based on spatial ranks in infinite-dimensional spaces, we investigate its asymptotic properties and compare it with several existing tests. The proposed test is shown to be robust with respect to outliers and to have better power than some competitors for certain distributions with heavy tails. We study its performance using real and simulated data.

Suggested Citation

  • Anirvan Chakraborty & Probal Chaudhuri, 2015. "A Wilcoxon–Mann–Whitney-type test for infinite-dimensional data," Biometrika, Biometrika Trust, vol. 102(1), pages 239-246.
    • Handle: RePEc:oup:biomet:v:102:y:2015:i:1:p:239-246.
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    File URL: http://hdl.handle.net/10.1093/biomet/asu072
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    Cited by:

    1. Smida, Zaineb & Cucala, Lionel & Gannoun, Ali & Durif, Ghislain, 2022. "A Wilcoxon-Mann-Whitney spatial scan statistic for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    2. Liu, Jiamin & Ma, Shuangge & Xu, Wangli & Zhu, Liping, 2022. "A generalized Wilcoxon–Mann–Whitney type test for multivariate data through pairwise distance," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    3. Graciela Estévez-Pérez & Philippe Vieu, 2021. "A new way for ranking functional data with applications in diagnostic test," Computational Statistics, Springer, vol. 36(1), pages 127-154, March.

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