考虑协变量有测量误差时变系数模型的估计问题。提出的方法不需要假定特定的误差模型结构或已知的误差方差，也不需要重复观测的数据。通过工具变量的辅助，首先对测量误差进行校正，从而得到真实观察变量的估计。然后用这个估计取代真实观察变量，利用变系数模型的估计方法得到函数系数的估计。证明了所提估计的渐近正态性。数值模拟结果表明本文提出的基于校正误差的方法比直接使用测量误差数据的方法有更好的有限样本性质。
In this work, we consider the estimation of the variable-coefficient model when the covariates are measured with error. We do not specify any model structure of the measurement error, and do not require the knowledge of the variance of measurement error. Furthermore, repeated measurement data are not necessary. With the help of the instrument variable, we calibrate the error and obtain an estimator of the true variable. We replace the true variable by its estimator and get an estimator of the coefficient function by applying the local linear smoothing method. We prove the asymptotic normality of the proposed estimator. The simulation results show that the proposed estimator performs better than the naive estimator.
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