Zhou Yong, Liang Hua
Institute of Applied Mathematics, Academy of Mathematics and System Science,Chinese Academy of Science, Beijing, China, 100080.
Ann Stat. 2009 Feb;37(1):427-458. doi: 10.1214/07-AOS561.
We study semiparametric varying-coefficient partially linear models when some linear covariates are not observed, but ancillary variables are available. Semiparametric profile least-square-based estimation procedures are developed for parametric and nonparametric components after we calibrate the error-prone covariates. Asymptotic properties of the proposed estimators are established. We also propose the profile least-square-based ratio test and Wald test to identify significant parametric and nonparametric components. To improve accuracy of the proposed tests for small or moderate sample sizes, Wild bootstrap version is also proposed to calculate the critical values. Intensive simulation experiments are conducted to illustrate the proposed approaches.
我们研究了在一些线性协变量未被观测到但辅助变量可用的情况下的半参数变系数部分线性模型。在我们校准了易出错的协变量之后，为参数和非参数分量开发了基于半参数轮廓最小二乘的估计程序。建立了所提出估计量的渐近性质。我们还提出了基于轮廓最小二乘的比率检验和Wald检验，以识别显著的参数和非参数分量。为了提高所提出的检验对于中小样本量的准确性，还提出了Wild自助法版本来计算临界值。进行了大量的模拟实验来说明所提出的方法。
