A Comparison of Testing Methods in Scalar-on-Function Regression

TL;DR

This paper reviews and compares various testing methods for assessing the relationship between functional covariates and scalar responses in scalar-on-function regression, highlighting their performance across different data scenarios.

Contribution

It provides a comprehensive overview and numerical comparison of existing testing methods for nullity and linearity hypotheses in scalar-on-function regression.

Findings

Methods perform differently depending on data density and noise levels.

Some tests are more robust in sparse or noisy data scenarios.

Illustration on Tecator dataset demonstrates practical applicability.

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 the 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.