Estimation of a semiparametric varying-coefficient partially linear errors-in-variables model
Estimation of a semiparametric varying-coefficient partially linear errors-in-variables model
复制标题
DOI：
10.1016/j.jmva.2005.03.002
复制
发表时间：
2006-02
影响因子：
1.6
通讯作者：
Jinhong You;Gemai Chen
中科院分区：
文献类型：
--
作者：
Jinhong You;Gemai Chen
本文研究了变系数部分线性回归模型的估计问题，它是部分线性回归模型和变系数回归模型的推广[Fan and Huang，Mandarpt，University of北卡罗来纳州，查佩尔山，USA，2002].我们专注于一些协变量的情况下，测量加性误差。当忽略测量误差时，通常的轮廓最小二乘和局部多项式估计分别导致参数和非参数分量的有偏估计。通过修正衰减，我们提出了一个修正的轮廓最小二乘估计的参数分量和局部多项式估计的非参数分量。我们证明了前者是相容的、渐近正态的，并且达到了重对数律的收敛速度，而后者达到了通常非参数回归的最优强收敛速度。此外，还开发了一个一致的估计的误差方差。这些结果可以用来进行渐近有效的统计推断。一些模拟研究进行了说明有限样本性能的估计。
This paper studies the estimation of a varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model [Fan and Huang, Manuscript, University of North Carolina, Chapel Hill, USA, 2002]. We focus on the case where some covariates are measured with additive errors. The usual profile least squares and local polynomial estimations lead to biased estimators of the parametric and nonparametric components, respectively, when measurement errors are ignored. By correcting the attenuation we propose a modified profile least squares estimator for the parametric component and a local polynomial estimator for the nonparametric component. We show that the former is consistent, asymptotically normal and achieves the rate in the law of the iterated logarithm, and the latter achieves the optimal strong convergence rate of the usual nonparametric regression. In addition, a consistent estimator is also developed for the error variance. These results can be used to make asymptotically valid statistical inferences. Some simulation studies are conducted to illustrate the finite sample performance of the proposed estimators.