Kruskal-Wallis Test for Functional Data Based on Random Projections Generated from a Simulation of a Brownian Motion

Abstract

The k-sample problem for functional data has been widely studied from theoretical and applied perspectives. In literature, Gaussianity of the generating process is generally assumed, which may be impractical in some situations. This work proposes an extension of the Kruskal-Wallis test to the case of functional data as an alternative to the problem of non- Gaussianity. The methodology used consisted of transforming each group's functional data into scalars using random projections and subsequently performing classical Kruskal-Wallis tests. The main results were the extension of the Kruskal-Wallis test to the case of functional data and the verification of its unbiased and consistency properties. Reducing dimensionality from random projections allows us to extend the classical Kruskal-Wallis test to the functional context and solve problems of non-Gaussianity and atypical observations.