  While there exists several inferential methods for analyzing functional data
in factorial designs, there is a lack of statistical tests that are valid (i)
in general designs, (ii) under non-restrictive assumptions on the data
generating process and (iii) allow for coherent post-hoc analyses. In
particular, most existing methods assume Gaussianity or equal covariance
functions across groups (homoscedasticity) and are only applicable for specific
study designs that do not allow for evaluation of interactions. Moreover, all
available strategies are only designed for testing global hypotheses and do not
directly allow a more in-depth analysis of multiple local hypotheses. To
address the first two problems (i)-(ii), we propose flexible integral-type test
statistics that are applicable in general factorial designs under minimal
assumptions on the data generating process. In particular, we neither postulate
homoscedasticity nor Gaussianity. To approximate the statistics' null
distribution, we adopt a resampling approach and validate it methodologically.
Finally, we use our flexible testing framework to (iii) infer several local
null hypotheses simultaneously. To allow for powerful data analysis, we thereby
take the complex dependencies of the different local test statistics into
account. In extensive simulations we confirm that the new methods are flexibly
applicable. Two illustrate data analyses complete our study. The new testing
procedures are implemented in the R package multiFANOVA, which will be
available on CRAN soon.
