Distribution-Free Pointwise Adjusted P-Values for Functional Hypotheses

TL;DR

This paper develops distribution-free methods for pointwise p-value adjustment in functional hypothesis testing, enabling more powerful and controlled inference at each point of a function without relying on distributional assumptions.

Contribution

It introduces novel distribution-free pointwise p-value adjustment techniques for envelope tests in functional data analysis, enhancing power and error control.

Findings

New distribution-free p-value adjustment methods demonstrated.

Application to brain cortical thickness data showed improved detection.

Methods effectively control familywise error rate in functional tests.

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.