Feature Screening in High Dimensional Regression with Endogenous Covariates

The most existing methods for feature screening and variable selection are based on the exogeneity assumption. Endogeneity, however, often arises in some cases, specially in high dimensional models. In the contexts of feature screening and variable selection, the endogeneity may cause the increase of false positive and false negative selections. To overcome the difficulty of dealing with high dimensionality and endogeneity, we first propose a new feature screening tool to measure the marginal utilities of the predictors and then introduce a two-stage regularization framework to identify important predictors. We demonstrate that when the number of predictors grows at an exponential rate of the sample size, the proposed procedure possesses the consistency in ranking. Simulation studies further illustrate that the proposed method has good numerical behaviors.