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In this paper we consider the problem of the estimation of the ψ-regression function when the covariates take values in an infinite dimensional space. Our main aim is to establish, under a stationary ergodic process assumption, the asymptotic normality of this estimate.

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.