Regression estimation by local polynomial fitting for multivariate data streams

In this paper we study a local polynomial estimator of the regression function and its derivatives. We propose a sequential technique based on a multivariate counterpart of the stochastic approximation method for successive experiments for the local polynomial estimation problem. We present our results in a more general context by considering the weakly dependent sequence of stream data, for which we provide an asymptotic bias-variance decomposition of the considered estimator. Additionally, we study the asymptotic normality of the estimator and we provide algorithms for the practical use of the method in data streams framework.