A median test for functional data. Issue 2 (3rd April 2022)

• Record Type: Journal Article
• Authors: Smida, Zaineb; Cucala, Lionel; Gannoun, Ali; Durif, Ghislain
• Is Part Of: Journal of nonparametric statistics. Volume 34:Issue 2(2022)
• Page Start: 520
• Page End: 553
• Publication Date: 2022-04-03
• Subjects: Functional data -- heavy-tailed distributions -- two-sample location test -- separable Hilbert space -- smooth Banach space; 60F17 -- 62G05 -- 62G10 -- 62G20; Nonparametric statistics -- Periodicals; 519.5
• DOI: 10.1080/10485252.2022.2064997
• Languages: English
• ISSNs: 1048-5252

Abstract

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 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.