High‐dimensional regression coefficient estimation by nuclear norm plus l1 norm penalization

We propose a new estimator of the regression coefficients for a high-dimensional linear regression model, which is de rived by replacing the sample predictor covariance matrix in the OLS estimator with a different predictor covariance matrix estimate obtained by a nuclear norm plus l1 norm penalization. We call the estimator ALCE-reg. We make a direct theoretical comparison of the expected mean square error of ALCE-reg with OLS and RIDGE. We show in a sim ulation study that ALCE-reg is particularly effective when both the dimension and the sample size are large, due to its ability to find a good compromise between the large bias of shrinkage estimators (like RIDGE and LASSO) and the large variance of estimators conditioned by the sample predictor covariance matrix (like OLS and POET).