Abstract:This study is mainly focused on the important feature selection and variable selection of ultra-high dimensional partial linear models with endogenous covariates. Firstly, in view of an elimination of the selective deviation of data endogeneity on feature selection, combined with the correlation structure of endogenous covariates and instrumental variables, a sufficient condition has thus been given to distinguish important covariates from unimportant covariates, followed by a proposed feature selection method to measure the marginal utility of variables. Secondly, a variable selection method is adopted for the identification of important covariates by using the proposed feature screening method, with a combination of the profile estimation idea and the two-stage regular estimation method. Finally, under certain regular conditions, the theory proves that the proposed variable selection method helps to eliminate the influence of data endogeneity on variable selection, thus ensuring the consistency of ranking the importance of covariates.