Two-sample tests for multivariate functional data with applications

Abstract

Multivariate functional data are frequently obtained in many scientific or industrial areas where several functions for a statistical unit are observed over time. It is often interesting to check if the mean vector functions of two multivariate functional samples are equal. To address this important issue, two global tests for the above two-sample problem for multivariate functional data are proposed and studied. Their asymptotic random expressions under the null and certain local alternative hypotheses are derived and their root-n consistencies are established. Simulation studies show that the proposed two tests generally have higher or not worse powers than some existing competitors. A real data application illustrates the proposed tests.