Abstract

This paper is concerned with the consistency of nonparametric regression model. For the weighted estimator of unknown regression function, the strong consistency, the complete consistency and the convergence rate of the complete consistency are investigated under some mild conditions. These results extend or improve the corresponding ones of Yang et al. (2018) for extended negatively dependent (END, for short) random variables to asymptotically almost negatively associated random variables. Also, the simulation study of the finite samples provided in this paper shows the validity of our results.

中文翻译：

---

渐近几乎负相关的随机变量非参数回归模型中加权估计的一致性

摘要

本文关注的是非参数回归模型的一致性。对于未知回归函数的加权估计量，研究了在某些温和条件下的强一致性，完全一致性以及完全一致性的收敛速度。这些结果扩展或改进了Yang等人的相应研究。（2018）将负相关性（简称END）的随机变量扩展为渐近几乎为负相关的随机变量。此外，本文提供的有限样本的仿真研究表明了我们的结果的有效性。