Modèle à indice fonctionnel simple

Abstract

This paper concerns a generalization of the “Single Index Model” when the explanatory variable is valued in an infinite dimensional space. Such model will be called the “Single Functional Index Model”. The main contribution of this study is to propose a functional framework which includes the classical vectorial case. Pointwise asymptotic properties are stated under less restrictive conditions on the law of the explanatory variable than what it is usually assumed in the vectorial case. To cite this article: F. Ferraty et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).