In this paper, we investigate the nonparametric regression model based on extended negatively dependent errors. Some consistency results for the estimator of the regression function g ( x ) are presented, including the rates of strong consistency and complete consistency, and the mean convergence. The results obtained in this paper improve and extend the corresponding ones of Yang and Wang (Acta Math Appl Sin 22(4):522–530, 1999 ) and Priestley and Chao (J R Stat Soc B 34:385–392, 1972 ). Finally, we present a numerical simulation study to verify the validity of the results established here.

中文翻译：

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关于非参数回归模型中 P-C 估计量的一致性

在本文中，我们研究了基于扩展负相关误差的非参数回归模型。给出了回归函数 g ( x ) 估计量的一些一致性结果，包括强一致性和完全一致性率，以及平均收敛性。本文获得的结果改进和扩展了 Yang 和 Wang (Acta Math Appl Sin 22(4):522–530, 1999 ) 和 Priestley and Chao (JR Stat Soc B 34:385–392, 1972) 的相应结果。最后，我们提出了一个数值模拟研究来验证这里建立的结果的有效性。