ABSTRACT In this paper, we consider the estimation and goodness-of-fit test of a semiparametric varying-coefficient partially linear (SVCPL) model when both responses and part of covariates are measured with error. It is assumed that the true variables are measurable functions of some auxiliary variables. The often-used assumptions on the measurement error, such as a known error variance, a known distribution of the error variable, a validation sample or a repeated data set, are not required. The asymptotic properties of the proposed estimators and testing statistic are investigated. We show that the application of the measurement error structures can improve the efficiency of estimating and testing methods. The performances of the estimating and testing methods are illustrated by simulation studies and an application to a real data set.

中文翻译：

---

改进的半参数变系数部分线性测量误差模型的统计推断

摘要 在本文中，我们考虑了当响应和部分协变量都测量有误差时半参数变系数部分线性 (SVCPL) 模型的估计和拟合优度检验。假设真实变量是一些辅助变量的可测函数。不需要经常使用的关于测量误差的假设，例如已知误差方差、已知误差变量分布、验证样本或重复数据集。研究了所提出的估计量和检验统计量的渐近特性。我们表明测量误差结构的应用可以提高估计和测试方法的效率。通过模拟研究和对真实数据集的应用来说明估计和测试方法的性能。