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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.

MSC:
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
Software:
fda.usc; nlme; fda (R); RLRsim
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References:
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