含测量误差的部分线性模型的发散参数估计

摘要

We consider partially linear models in which the linear covariate contains measurement errors,but insteadan observed surrogate that is linearly related to the unobserved covariate.Moreover,the dimension of unobserved covariate diverges with the sample size.We propose an estimation procedure and establish the consistency and asymptotic normality property of estimate.The rate of the divergent dimension is also investigated.A simulation study and a real data are carried out to illustrate the usefulness of the proposed method.%本文考虑了部分线性模型中,线性部分协变量含有测量误差,并且线性部分的参数随着样本量的增大而发散的估计问题.我们考虑了用可观测的替代变量来替代不可观察到的真实变量,这种替代变量的期望与真实变量存在线性关系我们提出了估计方法,并研究了估计量的相合性与渐进正态性.此外,我们研究了发散参数的发散速度.我们通过模拟来说明该估计的实际效果.