The functional nonparametric model and application to spectrometric data

The aim of this paper is to present a nonparametric regression model with scalar response when the explanatory variables are curves. In this context, the crucial problem of dimension reduction is overriden by the use of an implicit fractal dimension hypothesis. For such a functional nonparametric regression model we introduce and study both practical and theoretical aspects of some kernel type estimator. After a simulation study, it is shown how this procedure is well adapted to some spectrometric data set. Asymptotic results are described and in conclusion it turns out that this method combines advantages of easy implementation and good mathematical properties.