In this paper, a partially linear varying-coefficient model with measurement errors in the nonparametric component as well as missing response variable is studied. Two estimators for the parameter vector and nonparametric function are proposed based on the locally corrected profile least squares method. The first estimator is constructed by using the complete-case data only, and another by using an imputation technique. Both proposed estimators of the parametric component are shown to be asymptotically normal, and the estimators of nonparametric function are proved to achieve the optimal strong convergence rate as the usual nonparametric regression. Some simulation studies are conducted to compare the behavior of these estimators and the results confirm that the estimators based on the imputation technique perform better than the complete-case data estimator in finite samples. Finally, an application to a real data set is illustrated.

本文研究了具有非参数分量中的测量误差以及缺少响应变量的部分线性变化系数模型。基于局部校正轮廓最小二乘法，提出了参数向量和非参数函数的两个估计量。第一个估计器仅通过使用完整情况数据来构造，而另一个则通过使用插补技术来构造。两个建议的参数分量估计量都证明是渐近正态的，并且非参数函数的估计量被证明可以实现最佳的强收敛速度，这是通常的非参数回归。进行了一些模拟研究，以比较这些估计量的行为，结果证实，在有限样本中，基于插补技术的估计量要比完整情况下的数据估计量更好。最后，说明了对实际数据集的应用。