A median test for functional data. Issue 2 (3rd April 2022) - Smida, Zaineb; Cucala, Lionel; Gannoun, Ali; Durif, Ghislain
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.