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

We propose a new estimator of the regression coefficients for high-dimensional linear model, which is derived by replacing sample predictor covariance matrix in ordinary least square (OLS) with different estimate obtained nuclear norm plus l 1 penalization. call ALgebraic Covariance Estimator-regression (ALCE-reg). make direct theoretical comparison expected mean error ALCE-reg OLS and RIDGE. show simulation study that particularly effective when both dimension size are large, due to its ability find good compromise between large bias shrinkage estimators (like RIDGE absolute selection operator [LASSO]) variance conditioned principal orthogonal complement thresholding [POET]).