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Tests of Normality of Functional Data
Author(s) -
Górecki Tomasz,
Horváth Lajos,
Kokoszka Piotr
Publication year - 2020
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/insr.12362
Subject(s) - functional principal component analysis , normality , kurtosis , principal component analysis , multivariate statistics , sample (material) , normality test , mathematics , skewness , statistics , multivariate normal distribution , computer science , transformation (genetics) , statistical hypothesis testing , data mining , artificial intelligence , chemistry , biochemistry , chromatography , gene
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.