A one-way ANOVA test for functional data with graphical interpretation

Tomáš Mrkvička; Mari Myllymäki; Milan Jílek; Ute Hahn

Kybernetika (2020)

  • Volume: 56, Issue: 3, page 432-458
  • ISSN: 0023-5954

Abstract

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A new functional ANOVA test, with a graphical interpretation of the result, is presented. The test is an extension of the global envelope test introduced by Myllymäki et al. (2017, Global envelope tests for spatial processes, J. R. Statist. Soc. B 79, 381-404, doi: 10.1111/rssb.12172). The graphical interpretation is realized by a global envelope which is drawn jointly for all samples of functions. If a mean function computed from the empirical data is out of the given envelope, the null hypothesis is rejected with the predetermined significance level α . The advantages of the proposed one-way functional ANOVA are that it identifies the domains of the functions which are responsible for the potential rejection. We introduce two versions of this test: the first gives a graphical interpretation of the test results in the original space of the functions and the second immediately offers a post-hoc test by identifying the significant pair-wise differences between groups. The proposed tests rely on discretization of the functions, therefore the tests are also applicable in the multidimensional ANOVA problem. In the empirical part of the article, we demonstrate the use of the method by analyzing fiscal decentralization in European countries.

How to cite

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Mrkvička, Tomáš, et al. "A one-way ANOVA test for functional data with graphical interpretation." Kybernetika 56.3 (2020): 432-458. <http://eudml.org/doc/297118>.

@article{Mrkvička2020,
abstract = {A new functional ANOVA test, with a graphical interpretation of the result, is presented. The test is an extension of the global envelope test introduced by Myllymäki et al. (2017, Global envelope tests for spatial processes, J. R. Statist. Soc. B 79, 381-404, doi: 10.1111/rssb.12172). The graphical interpretation is realized by a global envelope which is drawn jointly for all samples of functions. If a mean function computed from the empirical data is out of the given envelope, the null hypothesis is rejected with the predetermined significance level $\alpha $. The advantages of the proposed one-way functional ANOVA are that it identifies the domains of the functions which are responsible for the potential rejection. We introduce two versions of this test: the first gives a graphical interpretation of the test results in the original space of the functions and the second immediately offers a post-hoc test by identifying the significant pair-wise differences between groups. The proposed tests rely on discretization of the functions, therefore the tests are also applicable in the multidimensional ANOVA problem. In the empirical part of the article, we demonstrate the use of the method by analyzing fiscal decentralization in European countries.},
author = {Mrkvička, Tomáš, Myllymäki, Mari, Jílek, Milan, Hahn, Ute},
journal = {Kybernetika},
keywords = {global envelope test; groups comparison; permutation test; Europe; fiscal decentralization; nonparametrical methods},
language = {eng},
number = {3},
pages = {432-458},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A one-way ANOVA test for functional data with graphical interpretation},
url = {http://eudml.org/doc/297118},
volume = {56},
year = {2020},
}

TY - JOUR
AU - Mrkvička, Tomáš
AU - Myllymäki, Mari
AU - Jílek, Milan
AU - Hahn, Ute
TI - A one-way ANOVA test for functional data with graphical interpretation
JO - Kybernetika
PY - 2020
PB - Institute of Information Theory and Automation AS CR
VL - 56
IS - 3
SP - 432
EP - 458
AB - A new functional ANOVA test, with a graphical interpretation of the result, is presented. The test is an extension of the global envelope test introduced by Myllymäki et al. (2017, Global envelope tests for spatial processes, J. R. Statist. Soc. B 79, 381-404, doi: 10.1111/rssb.12172). The graphical interpretation is realized by a global envelope which is drawn jointly for all samples of functions. If a mean function computed from the empirical data is out of the given envelope, the null hypothesis is rejected with the predetermined significance level $\alpha $. The advantages of the proposed one-way functional ANOVA are that it identifies the domains of the functions which are responsible for the potential rejection. We introduce two versions of this test: the first gives a graphical interpretation of the test results in the original space of the functions and the second immediately offers a post-hoc test by identifying the significant pair-wise differences between groups. The proposed tests rely on discretization of the functions, therefore the tests are also applicable in the multidimensional ANOVA problem. In the empirical part of the article, we demonstrate the use of the method by analyzing fiscal decentralization in European countries.
LA - eng
KW - global envelope test; groups comparison; permutation test; Europe; fiscal decentralization; nonparametrical methods
UR - http://eudml.org/doc/297118
ER -

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