Abstract In this article, an errors-in-variables regression model in which the errors are negatively superadditive dependent (NSD) random variables is studied. First, the Marcinkiewicz-type strong law of large numbers for NSD random variables is established. Then, we use the strong law of large numbers to investigate the asymptotic normality of least square (LS) estimators for the unknown parameters. In addition, the mean consistency of LS estimators for the unknown parameters is also obtained. Some results for independent random variables and negatively associated random variables are extended and improved to the case of NSD setting. At last, two simulations are presented to verify the asymptotic normality and mean consistency of LS estimators in the model.

中文翻译：

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具有相关误差的变量误差模型中 LS 估计量的渐近正态性和均值一致性

摘要 本文研究了一个误差为负超可加依赖（NSD）随机变量的变量误差回归模型。首先，建立了 NSD 随机变量的 Marcinkiewicz 型强大数定律。然后，我们使用强数定律来研究未知参数的最小二乘 (LS) 估计量的渐近正态性。此外，还获得了未知参数的 LS 估计量的平均一致性。一些独立随机变量和负相关随机变量的结果被扩展和改进到 NSD 设置的情况。最后，通过两次仿真验证模型中LS估计量的渐近正态性和均值一致性。