The Berry–Esseen-type bound for the G-M estimator in a nonparametric regression model with α-mixing errors

Abstract

Consider the fixed design nonparametric regression model: , where are known fixed design points from satisfying and is an unknown function defined on the closed interval , are the response variables, and are zero mean α-mixing random variables with , where . We derive the Berry–Esseen-type bound for the G-M estimator of under some mild conditions, which approximates to provided that weights and moments are appropriate. Our results generalize some known ones in the literature. In addition, a simulation study is given to illustrate the validity of the theoretical result.