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

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  • Tomáš Mrkvička, University of South Bohemia
  • ,
  • Mari Myllymäki, Natural Resources Institute Finland (Luke)
  • ,
  • Milan Jílek, University of South Bohemia
  • ,
  • Ute Hahn
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 Myllym ̈aki et al. (2017, Globalenvelope 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 sam-ples of functions. If a mean function computed from the empirical data is out of the givenenvelope, the null hypothesis is rejected with the predetermined significance levelα. The ad-vantages of the proposed one-way functional ANOVA are that it identifies the domains of thefunctions which are responsible for the potential rejection. We introduce two versions of thistest: the first gives a graphical interpretation of the test results in the original space of the func-tions and the second immediately offers a post-hoc test by identifying the significant pair-wisedifferences between groups. The proposed tests rely on discretization of the functions, thereforethe tests are also applicable in the multidimensional ANOVA problem. In the empirical partof the article, we demonstrate the use of the method by analyzing fiscal decentralization inEuropean countries
Original languageEnglish
Pages (from-to)432-458
Number of pages27
Publication statusPublished - 2020

    Research areas

  • Europe, Fiscal decentralization, Global envelope test, Groups comparison, Nonparametrical methods, Permutation test

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