Super-optimal rate of convergence in non-parametric estimation for functional valued processes

Christophe Chesneau (1) , Bertrand Maillot (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

In this paper, we consider the non-parametric estimation of the generalised regression function for continuous time processes with irregular paths when the regressor takes values in a semi-metric space. We establish the mean-square convergence of our estimator with the same super-optimal rate as when the regressor is real valued.

Mots clés: Regression estimation; Functional variables; Infinite dimensional space; Small balls probabilties.; Small balls probabilties

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Christophe Chesneau, Bertrand Maillot. Super-optimal rate of convergence in non-parametric estimation for functional valued processes. 2013. ⟨hal-00850123⟩