Regularization statistical inferences for partially linear models with high dimensional endogenous covariates

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.