Covariate measurement error is a common problem. Improper treatment of measurement errors may affect the quality of estimation and the accuracy of inference. Extensive literature exists on homoscedastic measurement error models, but little research exists on heteroscedastic measurement. In this paper, we consider a general parametric regression model allowing for a covariate measured with heteroscedastic error. We allow both the variance function of the measurement errors and the conditional density function of the error-prone covariate given the error-free covariates to be completely unspecified. We treat the variance function using B-spline approximation and propose a semiparametric estimator based on efficient score functions to deal with the heteroscedasticity of the measurement error. The resulting estimator is consistent and enjoys good inference properties. Its finite-sample performance is demonstrated through simulation studies and a real data example.

中文翻译：

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具有异方差误差的测量误差模型的半参数回归

协变量测量误差是一个常见问题。测量误差处理不当可能会影响估计的质量和推理的准确性。存在大量关于同方差测量误差模型的文献，但很少有关于异方差测量的研究。在本文中，我们考虑了一个通用参数回归模型，该模型允许使用异方差误差测量协变量。我们允许测量误差的方差函数和容易出错的协变量的条件密度函数给定无误差协变量完全未指定。我们使用 B 样条近似处理方差函数，并提出了一种基于有效得分函数的半参数估计器来处理测量误差的异方差性。由此产生的估计量是一致的，并享有良好的推理特性。其有限样本性能通过模拟研究和真实数据示例得以证明。