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.

本文讨论了一种新的估计器，它在惩罚回归方法的范围内同时执行参数估计和变量选择。估计量是 Liu 估计量的扩展，具有\(\ell _{1}\)- 规范惩罚。我们给出了坐标下降算法来有效地估计所提出的估计器的系数向量。我们还检查了估计器的一致性属性。我们进行了模拟研究和两个真实数据分析，以将提议的估计量与包括脊、刘、套索和弹性网在内的几个估计量进行比较。仿真研究和实际数据分析表明，新的估计器除了执行自动变量选择外，在稀疏和非稀疏数据结构下具有可观的预测性能和较小的均方误差。