We consider hypothesis testing with smooth functional data by performing
pointwise tests and applying a multiple comparisons procedure.
Methods based on general inequalities (such as Bonferroni's method)
do not perform well because of the high correlation between
observations at nearby points.
We consider the multiple comparison procedure proposed by
Westfall and Young (1993) and show that it approximates
a multiple comparison correction for a continuum of
comparisons as the grid for pointwise comparisons becomes
finer. Simulations and an application
verify that this result applies in practical
settings.
Keywords: Functional data analysis;
Hypothesis testing;
Multiple comparison procedure;
Permutation method.