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arXiv · 1912.00360

Distribution-Free Pointwise Adjusted P-Values for Functional Hypotheses

Meng Xu·Philip T. Reiss
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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.

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Meng Xu, Philip T. Reiss. 2019-12-01. Distribution-Free Pointwise Adjusted P-Values for Functional Hypotheses. https://doi.org/10.1007/978-3-030-47756-1_32

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