In this paper, we mainly investigate the nonparametric regression model with repeated measurements based on extended negatively dependent (END, in short) errors. Based on the Rosenthal type inequality and the Marcinkiewicz–Zygmund type strong law of large numbers, the mean consistency, weak consistency, strong consistency, complete consistency and strong convergence rate of the wavelet estimator are established under some mild conditions, which generalize the corresponding ones for negatively associated errors. Some numerical simulations are presented to verify the validity of the theoretical results.

中文翻译：

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非参数回归模型中小波估计量的一致性

在本文中，我们主要研究基于扩展负相关（END，简称 END）误差的具有重复测量的非参数回归模型。基于Rosenthal型不等式和Marcinkiewicz-Zygmund型强大数定律，在一些温和条件下建立了小波估计量的均值一致性、弱一致性、强一致性、完全一致性和强收敛率，并推广了相应的小波估计量对于负相关错误。给出了一些数值模拟来验证理论结果的有效性。