Pointwise testing with functional data using the Westfall-Young randomization method

We consider hypothesis testing with smooth functional data byperforming pointwise tests and applying a multiple comparisonsprocedure. Methods based on general inequalities, such as Bonferroni’smethod, do not perform well because of the high correlationbetween observations at nearby points. We consider the multiplecomparison procedure proposed by Westfall & Young (1993)and show that it approximates a multiple comparison correctionfor a continuum of comparisons as the grid for pointwise comparisonsbecomes finer. Simulations and an application verify that thisresult applies in practical settings.