中文摘要：

m-END随机变量是一类很弱的负相依随机变量,它包含了NA随机变量、NOD随机变量和END随机变量。本文基于误差为m-END序列,研究非参数回归模型未知参数的加权估计,获得了加权估计的收敛性,包括矩相合性收敛速度和完全相合性收敛速度。作为应用,给出非参数回归模型未知参数近邻权估计的矩相合性收敛速度和完全相合性收敛速度。

英文摘要：

m-END random variables are weakly dependent random variables, which contain NA random variables, NOD random variables and END random variables. In this paper, we investigate the weighted estimator of nonparametric regression model based on m-END errors. Some results of consistency such as mean convergence rate and complete convergence rate are obtained. As an application, the nearest neighbor weight estimator of nonparametric regression model is studied and mean convergence rate and complete convergence rate are presented.