Functional ANOVA based on empirical characteristic functionals

Functional two-sample tests based on empirical characteristic functionals are studied. We consider a test statistic of Cramer-von Mises type with integration over a preselected family of probability measures, say Q, leading to a computationally feasible and powerful test statistic. Small sample properties of the resulting two- and k-sample functional tests are investigated in a simulation study. In particular, we compare the resulting tests to previously proposed tests of equality of mean functions and covariance operators and we show that a proper choice of the probability measure Q gives very good power in detecting shift and scale alternatives. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

This paper studies functional two-sample tests based on empirical characteristic functionals, proposes a computationally feasible and powerful test statistic, and explores its small sample properties through simulation studies. The results show that, with the proper choice of probability measure, the proposed test can effectively detect shift and scale alternatives.