  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.
