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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Xu, M., Reiss, P.T. (2020). Distribution-free Pointwise Adjusted %-values for Functional Hypotheses. In: Aneiros, G., Horová, I., Hušková, M., Vieu, P. (eds) Functional and High-Dimensional Statistics and Related Fields. IWFOS 2020. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-030-47756-1_32
Download citation
DOI: https://doi.org/10.1007/978-3-030-47756-1_32
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-47755-4
Online ISBN: 978-3-030-47756-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)