As a generalization of additive model and partially linear model, partially linear additive model has been paid considerably attention in recent years. This paper considers estimation of the parametric component of the semiparametric model when the covariates in the linear part are measured with additive error and some additional stochastic linear restrictions on the parametric component are available. Based on the corrected profile least-squares approach and mixed regression estimation method, we propose a corrected profile mixed estimator for the parametric component, and derive its asymptotic distribution. Finally, some simulation studies are conducted to illustrate the proposed procedure and the results are satisfactory.

中文翻译：

---

部分线性加性变量模型中的随机受限估计

作为加法模型和部分线性模型的推广，部分线性加法模型近年来受到了广泛的关注。本文考虑了当线性部分中的协变量用加性误差测量并且对参数分量有一些额外的随机线性限制可用时，半参数模型的参数分量的估计。基于修正轮廓最小二乘法和混合回归估计方法，我们提出了参数分量的修正轮廓混合估计器，并推导出其渐近分布。最后，进行了一些仿真研究来说明所提出的程序，结果令人满意。