Resampling-based multiple comparison procedure with application to point-wise testing with functional data

Olga A. Vsevolozhskaya, Mark C. Greenwood, Scott L. Powell, Dmitri V. Zaykin

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

In this paper we describe a coherent multiple testing procedure for correlated test statistics such as are encountered in functional linear models. The procedure makes use of two different p value combination methods: the Fisher combination method and the Šidák correction-based method. p values for Fisher’s and Šidák’s test statistics are estimated through resampling to cope with the correlated tests. Building upon these two existing combination methods, we propose the smallest p value as a new test statistic for each hypothesis. The closure principle is incorporated along with the new test statistic to obtain the overall p value and appropriately adjust the individual p values. Furthermore, a shortcut version for the proposed procedure is detailed, so that individual adjustments can be obtained even for a large number of tests. The motivation for developing the procedure comes from a problem of point-wise inference with smooth functional data where tests at neighboring points are related. A simulation study verifies that the methodology performs well in this setting. We illustrate the proposed method with data from a study on the aerial detection of the spectral effect of below ground carbon dioxide leakage on vegetation stress via spectral responses.

Original languageEnglish
Pages (from-to)45-59
Number of pages15
JournalEnvironmental and Ecological Statistics
Volume22
Issue number1
DOIs
StatePublished - Mar 2015

Bibliographical note

Publisher Copyright:
© 2014, Springer Science+Business Media New York.

Keywords

  • Combining correlated p values
  • Functional data analysis
  • Multiple testing
  • Permutation procedure

ASJC Scopus subject areas

  • Statistics and Probability
  • General Environmental Science
  • Statistics, Probability and Uncertainty

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