Efficient Penalized Estimation for Linear Regression Model

This paper develops new penalized estimation for linear regression model. We prove that the new method, which is referred to as efficient penalized estimation, is selection consistent, and more asymptotically efficient than the original one. Besides, we construct a new selector called efficient BIC Selector to tune the regularization parameter in the new estimation, which is shown to be consistent. Our simulation results suggest that the new method may bring significant improvement relative to the original penalized estimation. In addition, we employ a real data set to illustrate the application of the efficient penalized estimation.