Tests of Normality of Functional Data. (17th February 2020)

• Record Type: Journal Article
• Authors: Górecki, Tomasz; Horváth, Lajos; Kokoszka, Piotr
• Is Part Of: International statistical review. Volume 88:Number 3(2020)
• Page Start: 677
• Page End: 697
• Publication Date: 2020-02-17
• Subjects: functional data -- normal distribution -- significance tests; Statistics -- Periodicals; Statistics -- Bibliography -- Periodicals; Statistics -- Bibliography; Statistics -- Periodicals; Statistique; Statistique -- Périodiques; Statistique -- Bibliographie -- Périodiques; Statistique -- Étude et enseignement -- Périodiques; Statistique -- Étude et enseignement -- Bibliographie -- Périodiques; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519.2
• DOI: 10.1111/insr.12362
• Languages: English
• ISSNs: 0306-7734

Abstract

Summary: 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.