In a linear mean regression setting with repeated measurement errors, we develop asymptotic properties of a naive estimator to better clarify the effects of these errors. We then construct a group of unbiased estimating equations with independent repetitions and make use of these equations in two ways to obtain two estimators: a weighted averaging estimator and an estimator based on the generalized method of moments. The proposed estimators do not require any additional information about the measurement errors. We also prove the consistency and asymptotic normality of the two estimators. Our theoretical results are verified by simulation studies and a real data analysis.

中文翻译：

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线性回归模型中重复测量误差的使用

在具有重复测量误差的线性平均回归设置中，我们开发了朴素估计量的渐近特性，以更好地阐明这些误差的影响。然后我们构造了一组具有独立重复的无偏估计方程，并以两种方式利用这些方程得到两个估计量：加权平均估计量和基于广义矩法的估计量。建议的估计器不需要关于测量误差的任何附加信息。我们还证明了两个估计量的一致性和渐近正态性。我们的理论结果通过模拟研究和真实数据分析得到验证。