Sequential adaptive estimators in nonparametric autoregressive models

Ouerdia Arkoun (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

We constuct a sequential adaptive procedure for estimating the autoregressive function at a given point in nonparametric autoregression models with Gaussian noise. We make use of the sequential kernel estimators. The optimal adaptive convergence rate is given as well as the upper bound for the minimax risk.

Mots clés: nonparametric autoregression; Adaptive estimation; kernel estimator; minimax; nonparametric autoregression.

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

Ouerdia Arkoun. Sequential adaptive estimators in nonparametric autoregressive models. 2010. ⟨hal-00465587v2⟩