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

doi:10.1016/j.csda.2013.05.005

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

Producción científica: Article › revisión exhaustiva

6 Citas (Scopus)

Resumen

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.

Idioma original	English
Páginas (desde-hasta)	175-184
Número de páginas	10
Publicación	Computational Statistics and Data Analysis
Volumen	67
DOI	https://doi.org/10.1016/j.csda.2013.05.005
Estado	Published - 2013

Nota bibliográfica

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.

Financiación

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.

Financiadores	Número del financiador
Michigan State University-U.S. Department of Energy (MSU-DOE) Plant Research Laboratory
National Energy Technology Laboratory

ASJC Scopus subject areas

Statistics and Probability
Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics

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10.1016/j.csda.2013.05.005

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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.",

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AU - Greenwood, M. C.

AU - Bellante, G. J.

AU - Powell, S. L.

AU - Lawrence, R. L.

AU - Repasky, K. S.

N1 - 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.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Distance-based method

KW - Functional data analysis

KW - Multiple comparison procedure

KW - Permutation method

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JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

ER -

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

Resumen

Nota bibliográfica

Financiación

ASJC Scopus subject areas

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