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The focus of functional data analysis has been mostly on independent functional observations. It is therefore hoped that the present contribution will provide an informative account of a useful approach that merges the ideas of the ergodic theory and the functional data analysis by using the local linear approach. More precisely, we aim, in this paper, to estimate the conditional distribution function (CDF) of a scalar response variable given a random variable taking values in a semimetric space. Under the ergodicity assumption, we study the uniform almost complete convergence (with a rate), as well as the asymptotic normality of the constructed estimator. The relevance of the proposed estimator is verified through a simulation study.

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.

This paper is devoted to the study of asymptotic properties of the kernel estimator of the robust regression function for stationary continuous‐time and ergodic data. Such a dependence structure is an alternative to the strong mixing conditions usually assumed in functional time series analysis. More precisely, we consider the kernel type estimator of the robust regression function constructed from the stationary and continuous‐time ergodic data false(Xt,Ytfalse) for 0≤t≤T. Then, we establish the almost sure (with rate) pointwise convergence of this estimator. A simulation study was conducted in order to compare the performance of this method to the classical regression method.