Berry-Esseen bounds of weighted kernel estimator for a nonparametric regression model based on linear process errors under a LNQD sequence

Abstract

Abstract In this paper, the authors investigate the Berry-Esseen bounds of weighted kernel estimator for a nonparametric regression model based on linear process errors under a LNQD random variable sequence. The rate of the normal approximation is shown as O ( n − 1 / 6 ) $O(n^{-1/6})$ under some appropriate conditions. The results obtained in the article generalize or improve the corresponding ones for mixing dependent sequences in some sense.

Keywords

• weighted kernel estimator
• LNQD sequence
• Berry-Esseen bound
• linear process