Regression on functional data: methodological approach with application to near-infrared spectrometry

Abstract

We consider the situation when one observes a scalar response and a functional variable as predictor. For instance, in our petroleum industry problem, the response is the octane number of a gasoline sample and the functional predictor is a curve representing its near-infrared spectrum. The statistician community developed numerous models for handling such datasets and we focus here on four regression models: two standards as the functional linear model and the functional nonparametric regression, and two recently developed: the functional projection pursuit regression and a parsimonious model involving a nonparametric variable selection method. Each of these models are implemented with two datasets containing near-infrared spectrometric curves. A comparative study of these models is provided in order to emphasize their possible advantages and drawbacks. At last, a simple but useful methodological approach is then proposed in order to boost the two most recent regression models by combining the most relevant informations obtained by each of the studied models. We show on the spectrometric data how such an approach may lead to important improvements.