Weighted Nadaraya-Watson regression estimation

In this article, we study nonparametric estimation of regression function by using the weighted Nadaraya-Watson approach. We establish the asymptotic normality and weak consistency of the resulting estimator for alpha -mixing time series at both boundary and interior points, and we show that the weighted Nadaraya-Watson estimator not only preserves the bias, variance, and more importantly, automatic good boundary behavior properties of local linear estimator, but also makes computation fast. Furthermore, the asymptotic minimax efficiency is discussed. Finally, comparisons between weighted Nadaraya-Watson approach and local linear fitting are given. (C) 2001 Elsevier Science B.V. All rights reserved. MSG: Primary 62G07; 62M10; secondary 62G20; 62F35.