Combining functions and the closure principle for performing follow-up tests in functional analysis of variance

Functional analysis of variance involves testing for differences in functional means across k groups in n functional responses. If a significant overall difference in the mean curves is detected, one may want to identify the location of these differences. Cox and Lee (2008) proposed performing a point-wise test and applying the Westfall–Young multiple comparison correction. We propose an alternative procedure for identifying regions of significant difference in the functional domain. Our procedure is based on a region-wise test and application of a combining function along with the closure multiplicity adjustment principle. We give an explicit formulation of how to implement our method and show that it performs well in a simulation study. The use of the new method is illustrated with an analysis of spectral responses related to vegetation changes from a CO2 release experiment.