A median test for functional data

Zaineb Smida (1) , Lionel Cucala (1) , Ali Gannoun (1) , Ghislain Durif (1)

1 IMAG - Institut Montpelliérain Alexander Grothendieck

The median test is more powerful than the Student t-test and the Wilcoxon-Mann-Whitney test in heavy-tailed cases for univariate data. When dealing with multidimensional data, the multivariate extension of the median test, called the sign test, is more efficient than the Hotelling T 2 and the Wilcoxon-Mann-Whitney tests for high dimensions and in very heavy-tailed cases. 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 the existing ones using simulated and real functional data.

Mots clés: Functional Data; Gâteaux Derivative; Heavy-Tailed Distributions; Two-Sample Location Test; Separable Hilbert Space; Smooth Banach Space AMS Subject Classifications: 60F17; 62G05; 62G10; 62G20

Domaines: Statistiques [stat]; Statistiques [math.ST]

Zaineb Smida, Lionel Cucala, Ali Gannoun, Ghislain Durif. A median test for functional data. 2022. ⟨hal-03560362v1⟩