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Selecting the derivative of a functional covariate in scalar-on-function regression

Abstract

This paper presents tests to formally choose between regression models using different derivatives of a functional covariate in scalar-on-function regression. We demonstrate that for linear regression, models using different derivatives can be nested within a model that includes point-impact effects at the end-points of the observed functions. Contrasts can then be employed to test the specification of different derivatives. When nonlinear regression models are employed, we apply a C test to determine the statistical significance of the nonlinear structure between a functional covariate and a scalar response. The finite-sample performance of these methods is verified in simulation, and their practical application is demonstrated using both chemometric and environmental data sets.

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Acknowledgements

The first author was partially supported by NSF grants DMS-1053252 and DEB-1353039. The second author acknowledges a sabbatical opportunity from the Research School of Finance, Actuarial Studies and Statistics at the Australian National University and the hospitality of the Department of Statistical Science at Cornell University. We would like to thank the associate editor and two anonymous referees for insightful comments that greatly improved the presentation of our results.

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Correspondence to Giles Hooker.

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Hooker, G., Shang, H.L. Selecting the derivative of a functional covariate in scalar-on-function regression. Stat Comput 32, 35 (2022). https://doi.org/10.1007/s11222-022-10091-5

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  • DOI: https://doi.org/10.1007/s11222-022-10091-5

Keywords

  • Model selection
  • Variable selection
  • Likelihood ratio test
  • C test