文摘
This Note focuses on an automatical choice of the functional parameter introduced throughout the single functional index model when one regresses a real r.v. on a functional r.v. (i.e. valued in an infinite-dimensional space). This Note aims to prove that a cross-validation-based method leads to an asymptotic optimal choice of the functional index. In addition, one states that such a choice for the functional index is a consistent estimator. To cite this article: A. Ait-Saïdi et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).