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

Author

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  • Merve Yasemin Tekbudak

    (North Carolina State University
    North Carolina State University)

  • Marcela Alfaro-Córdoba

    (Universidad de Costa Rica)

  • Arnab Maity

    (North Carolina State University)

  • Ana-Maria Staicu

    (North Carolina State University)

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.

Suggested Citation

  • Merve Yasemin Tekbudak & Marcela Alfaro-Córdoba & Arnab Maity & Ana-Maria Staicu, 2019. "A comparison of testing methods in scalar-on-function regression," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(3), pages 411-436, September.
    • Handle: RePEc:spr:alstar:v:103:y:2019:i:3:d:10.1007_s10182-018-00337-x
    DOI: 10.1007/s10182-018-00337-x
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    References listed on IDEAS

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    3. Eduardo García‐Portugués & Javier Álvarez‐Liébana & Gonzalo Álvarez‐Pérez & Wenceslao González‐Manteiga, 2021. "A goodness‐of‐fit test for the functional linear model with functional response," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 502-528, June.

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