Asymptotic normality of kernel estimates in a regression model for random fields

Mohamed El Machkouri (1) , Radu Stoica (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

We establish the asymptotic normality of the regression estimator in a fixed-design setting when the errors are given by a field of dependent random variables. The result applies to martingale-difference or strongly mixing random fields. On this basis, a statistical test that can be applied to image analysis is also presented.

Mots clés: Nonparametric regression estimation; asymptotic normality; kernel estimator; strongly mixing random field

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

Mohamed El Machkouri, Radu Stoica. Asymptotic normality of kernel estimates in a regression model for random fields. 2009. ⟨hal-00403055⟩