The Berry–Esseen type bounds of the weighted estimator in a nonparametric model with linear process errors

Abstract

In this paper, the Berry–Esseen type bounds of the weighted estimator in a nonparametric regression model are investigated under some mild conditions when random errors are from a linear process generated by $$\varphi $$ -mixing random variables. In particular, the rate of uniform normal approximation is near to $$O(n^{-\frac{3}{16}})$$ by the choice of some constants, which generalizes and improves the corresponding results of Li et al. (Stat Probab Lett 81:103–110, 2011) and Ding et al. (J Inequal Appl 2018:10, 2018). Finally, the simulation study is provided to verify the validity of the theoretical results.