a b s t r a c tWe propose a family of robust nonparametric estimators for a regression function based on the kernel method. We establish the asymptotic normality of the estimator under the concentration property on small balls probability measure of the functional explanatory variable when the observations exhibit some kind of dependence. This approach can be applied in time series analysis to make prediction and build confidence bands. We illustrate our methodology on the US electricity consumption data.
We propose a nonparametric predictor and a supervised classification based on the regression function estimate of a spatial real variable using k-nearest neighbors method (k-NN). Under some assumptions, we establish almost complete or sure convergence of the proposed estimates which incorporate a spatial proximity between observations. Numerical results on simulated and real fish data illustrate the behavior of the given predictor and classification method.
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