Bootstrap-Based K-Sample Testing for Functional Data

We investigate properties of a bootstrap-based methodology for testing hypotheses about equality of certain characteristics of the distributions between different populations in the context of functional data. The suggested testing methodology is simple and easy to implement. It resamples the original dataset in such a way that the null hypothesis of interest is satisfied and it can be potentially applied to a wide range of testing problems and test statistics of interest. Furthermore, it can be utilized to the case where more than two populations of functional data are considered. We illustrate the bootstrap procedure by considering the important problems of testing the equality of mean functions or the equality of covariance functions (resp. covariance operators) between two populations. Theoretical results that justify the validity of the suggested bootstrap-based procedure are established. Furthermore, simulation results demonstrate very good size and power performances in finite sample situations, including the case of testing problems and/or sample sizes where asymptotic considerations do not lead to satisfactory approximations. A real-life dataset analyzed in the literature is also examined.