Rate Optimal Estimation And Confidence Intervals For High-Dimensional Regression With Missing Covariates

We consider the problems of estimation and of constructing component-wise confidence intervals in a sparse high-dimensional linear regression model when some covariates of the design matrix are missing completely at random. We analyze a variant of the Dantzig selector for estimating the regression model and we use a de-biasing argument to construct component-wise confidence intervals. We also complement our mathematical study in the supplementary materials with extensive simulations on synthetic and semisynthetic data that show the accuracy of our asymptotic predictions for finite sample sizes. (C) 2019 Published by Elsevier Inc.