Two Stage Non-penalized Corrected Least Squares for High Dimensional Linear Models with Measurement error or Missing Covariates

Understand

This paper provides an alternative to penalized estimators for estimation and vari- able selection in high dimensional linear regression models with measurement error or missing covariates.

• We propose estimation via bias corrected least squares after model selection.
• We show that by separating model selection and estimation, it is possible to achieve an improved rate of convergence of the L2 estimation error compared to the rate sqrt{s log p/n} achieved by simultaneous estimation and variable selection methods such as L1 penalized corrected least squares.
• If the correct model is selected with high probability then the L2 rate of convergence for the proposed method is indeed the oracle rate of sqrt{s/n}.