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 is an element of NN) (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. (C) 2010 Elsevier B.V. All rights reserved.