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 $$\varphi $$φ-mixing random variables. In particular, the rate of uniform normal approximation is near to $$O(n^{-\frac{3}{16}})$$O(n-316) 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.

中文翻译：

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具有线性过程误差的非参数模型中加权估计量的 Berry-Esseen 类型边界

在本文中，当随机误差来自由 $$\varphi $$φ 混合随机变量生成的线性过程时，非参数回归模型中加权估计量的 Berry-Esseen 类型边界在一些温和条件下进行了研究。特别是，通过选择一些常数，均匀正态逼近的比率接近 $$O(n^{-\frac{3}{16}})$$O(n-316)，它概括和改进了Li等人的相应结果。(Stat Probab Lett 81:103–110, 2011) 和 Ding 等人。(J Inequal Appl 2018:10, 2018)。最后,通过仿真研究验证了理论结果的有效性。