Note on nonparametric M-estimation for spatial regression

Abstract

In this paper, we investigate a nonparametric robust estimation for spatial regression. More precisely, given a strictly stationary random field $Z_{\mathbf{i}}=\left(X_{\mathbf{i}}, Y_{\mathbf{i}}\right), \mathbf{i} \in \mathbb{N}^N$, we consider a family of robust nonparametric estimators for a regression function based on the kernel method. We establish a $p$-mean consistency results of the kernel estimator under some conditions.