Pointwise Testing with Functional Data Using the Westfall-Young Randomization Method

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.