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A Nonparametric Graphical Tests of Significance in Functional GLM

Author

Listed:
  • Tomáš Mrkvička

    (University of South Bohemia)

  • Tomáš Roskovec

    (University of South Bohemia)

  • Michael Rost

    (University of South Bohemia)

Abstract

A new nonparametric graphical test of significance of a covariate in functional GLM is proposed. Our approach is especially interesting due to its functional graphical interpretation of the results. As such, it is able to find not only if the factor of interest is significant but also which functional domain is responsible for the potential rejection. In the case of functional multi-way main effect ANOVA or functional main effect ANCOVA models it is able to find which groups differ (and where they differ), in the case of functional factorial ANOVA or functional factorial ANCOVA models it is able to find which combination of levels (which interactions) differ (and where they differ). The described tests are extensions of global envelope tests in the GLM models. It applies Freedman-Lane algorithm for the permutation of functions, and as such, it approximately achieves the desired significance level.

Suggested Citation

  • Tomáš Mrkvička & Tomáš Roskovec & Michael Rost, 2021. "A Nonparametric Graphical Tests of Significance in Functional GLM," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 593-612, June.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:2:d:10.1007_s11009-019-09756-y
    DOI: 10.1007/s11009-019-09756-y
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    References listed on IDEAS

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    1. Mari Myllymäki & Tomáš Mrkvička & Pavel Grabarnik & Henri Seijo & Ute Hahn, 2017. "Global envelope tests for spatial processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 381-404, March.
    2. Febrero-Bande, Manuel & de la Fuente, Manuel Oviedo, 2012. "Statistical Computing in Functional Data Analysis: The R Package fda.usc," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i04).
    3. Ferraty, Frederic & Vieu, Philippe & Viguier-Pla, Sylvie, 2007. "Factor-based comparison of groups of curves," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4903-4910, June.
    4. Freedman, David & Lane, David, 1983. "A Nonstochastic Interpretation of Reported Significance Levels," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(4), pages 292-298, October.
    5. Ute Hahn, 2012. "A Studentized Permutation Test for the Comparison of Spatial Point Patterns," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 754-764, June.
    6. J. Cuesta-Albertos & M. Febrero-Bande, 2010. "A simple multiway ANOVA for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 537-557, November.
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