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 defined, we apply a 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 a chemometric data set.
Keywords
Cite
@article{arxiv.2008.07859,
title = {Selecting the Derivative of a Functional Covariate in Scalar-on-Function Regression},
author = {Giles Hooker and Hanlin Shang},
journal= {arXiv preprint arXiv:2008.07859},
year = {2020}
}