Combining functions and the closure principle for performing follow-up tests in functional analysis of variance

O. A. Vsevolozhskaya, M. C. Greenwood, G. J. Bellante, S. L. Powell, R. L. Lawrence, K. S. Repasky

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Functional analysis of variance involves testing for differences in functional means across k groups in n functional responses. If a significant overall difference in the mean curves is detected, one may want to identify the location of these differences. Cox and Lee (2008) proposed performing a point-wise test and applying the Westfall-Young multiple comparison correction. We propose an alternative procedure for identifying regions of significant difference in the functional domain. Our procedure is based on a region-wise test and application of a combining function along with the closure multiplicity adjustment principle. We give an explicit formulation of how to implement our method and show that it performs well in a simulation study. The use of the new method is illustrated with an analysis of spectral responses related to vegetation changes from a CO2 release experiment.

Original languageEnglish
Pages (from-to)175-184
Number of pages10
JournalComputational Statistics and Data Analysis
StatePublished - 2013

Bibliographical note

Funding Information:
The authors would like to thank the two anonymous referees for their valuable feedback on the manuscript. Additional feedback from Megan Higgs and Jim Robison-Cox was very helpful. This work was carried out within the ZERT II project, with the support of the U.S. Department of Energy and the National Energy Technology Laboratory, under Award No. DE-FE0000397. However, any opinions, findings, conclusions, or recommendations expressed herein are those of the author(s) and do not necessarily reflect the views of the DOE.


  • Distance-based method
  • Functional data analysis
  • Multiple comparison procedure
  • Permutation method

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics


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