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

Yining Wang, Jialei Wang, Sivaraman Balakrishnan and Aarti Singh

Journal of Multivariate Analysis, 2019, vol. 174, issue C

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.

Keywords: Dantzig selector; De-biasing; High-dimensional regression; Missing data; Confidence intervals; Minimax rates (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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DOI: 10.1016/j.jmva.2019.06.004

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