This paper discusses simultaneous parameter estimation and variable selection and presents a new penalized regression method. The method is based on the idea that the coefficient estimates are shrunken towards a predetermined coefficient vector which represents the prior information. This method can result in smaller length estimates of the coefficients depending on the prior information compared to elastic net. In addition to the establishment of the grouping property, we also show that the new method has the grouping effect when the predictors are highly correlated. Simulation studies and real data example show that the prediction performance of the new method is improved over the well-known ridge, lasso and elastic net regression methods yielding a lower mean squared error and competes about the variable selection under sparse and non-sparse situations.

本文讨论了同时参数估计和变量选择，并提出了一种新的惩罚回归方法。该方法基于这样的思想，即系数估计朝着表示先前信息的预定系数向量缩小。与弹性网相比，该方法可以根据先验信息得出较小的系数长度估计。除了建立分组属性外，我们还表明，当预测变量高度相关时，新方法具有分组效果。仿真研究和实际数据示例表明，该新方法的预测性能比众所周知的山脊高，