Recursive regression estimators with application to nonparametric prediction

Abstract

In the case of dependent data, the purpose of this paper is to establish the exact asymptotic quadratic error of a parametric family of recursive kernel regression estimators. Based on this family of estimators, recursive nonparametric kernel predictors are studied. For mixing Markov processes, their almost sure convergence to the best predictor is established. Efficiency of these methods is also shown through numerical simulations highlighting their significantly reduced time of computation.