Rate optimal estimation and confidence intervals for high-dimensional regression with missing covariates

Yining Wang, Jialei Wang, Sivaraman Balakrishnan, Aarti Singh

Abstract: 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 semi-synthetic data that show the accuracy of our asymptotic predictions for finite sample sizes. Previous article in issue Next article in issue AMS 2000 subject classifications primary 62J05 secondary 62N01