A comparison of testing methods in scalar-on-function regression

Merve Yasemin Tekbudak (), Marcela Alfaro-Córdoba (), Arnab Maity () and Ana-Maria Staicu ()
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Merve Yasemin Tekbudak: North Carolina State University
Marcela Alfaro-Córdoba: Universidad de Costa Rica
Arnab Maity: North Carolina State University
Ana-Maria Staicu: North Carolina State University

AStA Advances in Statistical Analysis, 2019, vol. 103, issue 3, No 5, 436 pages

Abstract: Abstract 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.

Keywords: Functional regression; Functional linear model; Nonparametric regression; Mixed-effects model; Hypothesis testing (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10182-018-00337-x

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