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.
Published Version
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