Robust nonparametric estimation for spatial regression

In this paper, we investigate a nonparametric robust estimation for spatial regression. More precisely, given a strictly stationary random field Z i = ( X i , Y i ) i ∈ N N N ≥ 1 , we consider a family of robust nonparametric estimators for a regression function based on the kernel method. Under some general mixing assumptions, the almost complete consistency and the asymptotic normality of these estimators are obtained. A robust procedure to select the smoothing parameter adapted to the spatial data is also discussed.