A new double-regularized regression using Liu and lasso regularization

This paper discusses a new estimator that performs simultaneous parameter estimation and variable selection in the scope of penalized regression methods. The estimator is an extension of the Liu estimator with $$\ell _{1}$$ -norm penalization. We give the coordinate descent algorithm to estimate the coefficient vector of the proposed estimator, efficiently. We also examine the consistency properties of the estimator. We conduct simulation studies and two real data analyses to compare the proposed estimator with several estimators including the ridge, Liu, lasso and elastic net. The simulation studies and real data analyses show that besides performing automatic variable selection, the new estimator has considerable prediction performance with a small mean squared error under sparse and non-sparse data structures.