Convergence de l'estimateur à noyau des k plus proches voisins en régression fonctionnelle non-paramétrique

This note focuses on the k nearest neighbor method when one regresses a real random variable on a functional random variable (i.e. valued in an infinite-dimensional space). More precisely, we consider a kernel estimator of the regression based on a local bandwidth using exactly the k nearest neighbors. Although it is frequently used in functional data analysis, this method has not given any theoretical result so far. The aim of this Note is to show the pointwise almost-complete convergence of the k nearest neighbor kernel estimator in nonparametric functional regression. To cite this article: F. Burba et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).