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Recursive estimation of nonparametric regression with functional covariate (1211.2780v2)
Published 12 Nov 2012 in math.ST and stat.TH
Abstract: The main purpose is to estimate the regression function of a real random variable with functional explanatory variable by using a recursive nonparametric kernel approach. The mean square error and the almost sure convergence of a family of recursive kernel estimates of the regression function are derived. These results are established with rates and precise evaluation of the constant terms. Also, a central limit theorem for this class of estimators is established. The method is evaluated on simulations and real data set studies.