In this paper, we consider the statistical inferences for a class of partially linear models with high dimensional endogenous covariates, when high dimensional instrumental variables are also available. A regularized estimation procedure is proposed for identifying the optimal instrumental variables, and estimating covariate effects of the parametric and nonparametric components. Under some conditions, some theoretical properties are studied, such as the consistency of the optimal instrumental variable identification and significant covariate selection. Furthermore, some simulation studies and a real data analysis are carried out to examine the finite sample performance of the proposed method.

在本文中，当高维工具变量也可用时，我们考虑一类具有高维内生协变量的部分线性模型的统计推断。提出了一种正则估计程序，用于识别最佳工具变量，并估计参数和非参数分量的协变量效应。在某些条件下，研究了一些理论属性，例如最佳工具变量识别的一致性和重要的协变量选择。此外，进行了一些仿真研究和真实数据分析，以检验该方法的有限样本性能。