Nonparametric regression estimation for random fields in a fixed-design

Mohamed El Machkouri (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

We investigate the nonparametric estimation for regression in a fixed-design setting when the errors are given by a field of dependent random variables. Sufficient conditions for kernel estimators to converge uniformly are obtained. These estimators can attain the optimal rates of uniform convergence and the results apply to a large class of random fields which contains martingale-difference random fields and mixing random fields.

Mots clés: Orlicz spaces; fixed-design; mixing; exponential inequalities; strong consistency; nonparametric regression estimation; kernel estimators; martingale-difference random fields

Domaines: Statistiques [math.ST]; Probabilités [math.PR]

Mohamed El Machkouri. Nonparametric regression estimation for random fields in a fixed-design. Statistical Inference for Stochastic Processes, 2007. ⟨hal-00004096⟩