An $\{l_1,l_2,l_{\infty}\}$-Regularization Approach to High-Dimensional Errors-in-variables Models

Understand

Several new estimation methods have been recently proposed for the linear regression model with observation error in the design.

• Different assumptions on the data generating process have motivated different estimators and analysis.
• In particular, the literature considered (1) observation errors in the design uniformly bounded by some $\bar \delta$, and (2) zero mean independent observation errors.
• Under the first assumption, the rates of convergence of the proposed estimators depend explicitly on $\bar \delta$, while the second assumption has been applied when an estimator for the second moment of the observational error is available.