Distribution-Free Pointwise Adjusted P-Values for Functional Hypotheses
Abstract
Graphical tests assess whether a function of interest departs from an envelope of functions generated under a simulated null distribution. This approach originated in spatial statistics, but has recently gained some popularity in functional data analysis. Whereas such envelope tests examine deviation from a functional null distribution in an omnibus sense, in some applications we wish to do more: to obtain p-values at each point in the function domain, adjusted to control the familywise error rate. Here we derive pointwise adjusted p-values based on envelope tests, and relate these to previous approaches for functional data under distributional assumptions. We then present two alternative distribution-free p-value adjustments that offer greater power. The methods are illustrated with an analysis of age-varying sex effects on cortical thickness in the human brain.
Cite
@article{arxiv.1912.00360,
title = {Distribution-Free Pointwise Adjusted P-Values for Functional Hypotheses},
author = {Meng Xu and Philip T. Reiss},
journal= {arXiv preprint arXiv:1912.00360},
year = {2020}
}