A median test for functional data

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.

Keywords:

• Functional data
• heavy-tailed distributions
• two-sample location test
• separable Hilbert space
• smooth Banach space

AMS Subject Classifications:

• 60F17
• 62G05
• 62G10
• 62G20

Disclosure statement

No potential conflict of interest was reported by the author(s).