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Tests of Normality of Functional Data

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  • Tomasz Górecki
  • Lajos Horváth
  • Piotr Kokoszka

Abstract

The paper is concerned with testing normality in samples of curves and error curves estimated from functional regression models. We propose a general paradigm based on the application of multivariate normality tests to vectors of functional principal components scores. We examine finite sample performance of a number of such tests and select the best performing tests. We apply them to several extensively used functional data sets and determine which can be treated as normal, possibly after a suitable transformation. We also offer practical guidance on software implementations of all tests we study and develop large sample justification for tests based on sample skewness and kurtosis of functional principal component scores.

Suggested Citation

  • Tomasz Górecki & Lajos Horváth & Piotr Kokoszka, 2020. "Tests of Normality of Functional Data," International Statistical Review, International Statistical Institute, vol. 88(3), pages 677-697, December.
    • Handle: RePEc:bla:istatr:v:88:y:2020:i:3:p:677-697
    DOI: 10.1111/insr.12362
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    References listed on IDEAS

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    Cited by:

    1. Bruno Ebner & Norbert Henze, 2020. "Tests for multivariate normality—a critical review with emphasis on weighted $$L^2$$ L 2 -statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 845-892, December.
    2. Golovkine, Steven & Klutchnikoff, Nicolas & Patilea, Valentin, 2022. "Clustering multivariate functional data using unsupervised binary trees," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).

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