The multivariate Révész’s online estimator of a regression function and its averaging

Abstract

The first aim of this paper is to generalize the online estimator of a regression function introduced by Révész [26, 27] to the multivariate framework. Similarly to the univariate framework, the study of the convergence rate of the multivariate Révész’s estimator requires a tedious condition connecting the stepsize of the algorithm and the unknown value of the density of the regressor variable at the point at which the regression function is estimated. The second aim of this paper is to apply the averaging principle of stochastic approximation algorithms to remove this tedious condition.