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

Author

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

Abstract

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.

Suggested Citation

  • Vsevolozhskaya, O.A. & Greenwood, M.C. & Bellante, G.J. & Powell, S.L. & Lawrence, R.L. & Repasky, K.S., 2013. "Combining functions and the closure principle for performing follow-up tests in functional analysis of variance," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 175-184.
    • Handle: RePEc:eee:csdana:v:67:y:2013:i:c:p:175-184
    DOI: 10.1016/j.csda.2013.05.005
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    References listed on IDEAS

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    1. J. C. Gower & W. J. Krzanowski, 1999. "Analysis of distance for structured multivariate data and extensions to multivariate analysis of variance," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(4), pages 505-519.
    2. Dennis D. Cox & Jong Soo Lee, 2008. "Pointwise testing with functional data using the Westfall--Young randomization method," Biometrika, Biometrika Trust, vol. 95(3), pages 621-634.
    3. Cuevas, Antonio & Febrero, Manuel & Fraiman, Ricardo, 2004. "An anova test for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 47(1), pages 111-122, August.
    4. Pedro Delicado, 2007. "Functional k-sample problem when data are density functions," Computational Statistics, Springer, vol. 22(3), pages 391-410, September.
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    Cited by:

    1. Pini, Alessia & Sørensen, Helle & Tolver, Anders & Vantini, Simone, 2023. "Local inference for functional linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).

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