Double penalized regularization estimation for partially linear instrumental variable models with ultrahigh dimensional instrumental variables

Under ultrahigh dimensional instrumental variables, we consider the estimation for a class of partially linear models with endogenous covariates. To overcome the difficulty of ultrahigh dimensionality of the instrumental variables, we propose a double penalized regularization estimation procedure for identifying the optimal instrumental variables, and estimating covariate effects of the parametric and nonparametric components. With some regularity conditions, some asymptotic properties of the proposed estimation are derived, such as the consistency of the resulting estimators for parametric and nonparametric components. Lastly, we examine the finite sample performance of the proposed method by some simulation studies and a real data analysis.