Sélection automatique du paramètre de lissage pour l'estimation non paramétrique de la régression pour des données fonctionnelles

Abstract

We study regression estimation when the explanatory variable is functional. Nonparametric estimates of the regression operator have been recently introduced. They depend on a smoothing factor which controls its behaviour, and the aim of our Note is to construct some data-driven criterion for choosing this smoothing parameter. The criterion can be formulated in terms of a functional version of cross-validation ideas. Under mild assumptions on the unknown regression operator, it is seen that this rule is asymptotically optimal. As by-products of this result, we state asymptotic equivalences for several measures of accuracy for nonparametric estimate of the regression operator. To cite this article: M. Rachdi, P. Vieu, C. R. Acad. Sci. Paris, Ser. I 341 (2005).