A Kruskal-Wallis type test for functional data

Abstract

We present a non-parametric method to decide whether K independent samples of functional data have the same location parameter. To do so, random projections are used to transform functional data into univariate data and a Kruskal Wallis test is then applied in order to solve the one-dimensional problem. The p-values obtained from different projections are combined by applying the False Discovery Rate correction, giving rise to a new procedure that solves the functional problem. The method is explored through synthetic data and analyzing two real data sets.