A median test for functional data

Zaineb Smida, Lionel Cucala, Ali Gannoun and Ghislain Durif

Journal of Nonparametric Statistics, 2022, vol. 34, issue 2, 520-553

Abstract: The median test has been proven to be more powerful than the Student t-test and the Wilcoxon–Mann–Whitney test in heavy-tailed cases for univariate data. The multivariate extension of the median test, for multidimensional data, was demonstrated to be more efficient than the Hotelling $ T^{2} $ T2 and the Wilcoxon–Mann–Whitney tests for high dimensions and in very heavy-tailed cases. On the basis of these postulates, in this paper, we construct a median-type test based on spatial ranks for functional data, i.e. in infinite-dimensional space, and we obtain asymptotic results. Then, we compare the proposed functional median test with numerous competing tests using simulated and real functional data: as in the univariate and multivariate cases, the proposed test is more adapted to heavy-tailed distributions.

Date: 2022
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DOI: 10.1080/10485252.2022.2064997

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