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Biometrika Advance Access published online on July 23, 2008
Biometrika, doi:10.1093/biomet/asn021
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© 2008 Biometrika Trust

Article

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

Dennis D. Cox

Department of Statistics, Rice University, 6100 Main St. MS-138, Houston, Texas 77005, U.S.A. dcox{at}stat.rice.edu

Jong Soo Lee

Department of Statistics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, U.S.A. jslee{at}stat.cmu.edu

Received for publication 1 January 2007. Revision received 1 January 2008.
  Abstract

We consider hypothesis testing with smooth functional data by performing pointwise tests and applying a multiple comparisons procedure. Methods based on general inequalities, such as Bonferroni’s method, do not perform well because of the high correlation between observations at nearby points. We consider the multiple comparison procedure proposed by Westfall & Young (1993) and show that it approximates a multiple comparison correction for a continuum of comparisons as the grid for pointwise comparisons becomes finer. Simulations and an application verify that this result applies in practical settings.

Key Words: Functional data analysis • Hypothesis testing • Multiple comparison procedure • Permutation method.


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