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A comparison of testing methods in scalar-on-function regression. (English) Zbl 1427.62034
Summary: A scalar-response functional model describes the association between a scalar response and a set of functional covariates. An important problem in the functional data literature is to test nullity or linearity of the effect of the functional covariate in the context of scalar-on-function regression. This article provides an overview of the existing methods for testing both the null hypotheses that there is no relationship and that there is a linear relationship between the functional covariate and scalar response, and a comprehensive numerical comparison of their performance. The methods are compared for a variety of realistic scenarios: when the functional covariate is observed at dense or sparse grids and measurements include noise or not. Finally, the methods are illustrated on the Tecator data set.

62G08 Nonparametric regression and quantile regression
62G10 Nonparametric hypothesis testing
62R10 Functional data analysis
62P10 Applications of statistics to biology and medical sciences; meta analysis
62P30 Applications of statistics in engineering and industry; control charts
fda.usc; nlme; fda (R); RLRsim
Full Text: DOI
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