高维Extremile回归中变量选择的类弹性网惩罚方法

Variable selection in high-dimensional extremile regression via the quasi elastic net

近几年提出的Extremile回归不仅保留了分位数回归通过设定不同的分位点全面掌握数据信息的优点,而且与分位数回归中和Expectile回归相比也有其独特的优势,特别是在风险保护上的优秀表现。本文提出了一种带惩罚的线性Extremile回归模型用以解决高维数据下的变量选择问题,其中惩罚函数是由和惩罚函数组合得到的类弹性网(QEN)惩罚函数,同时给出了解决相关优化问题的EM算法,以及在较为宽松条件下即能成立相关理论性质。在数值模拟中,我们通过与L_(0),L_(1),L_(2)和弹性网惩罚函数的比较,展示了类弹性网惩罚函数。

Extremile regression proposed in recent years not only retains the advantage of quantile regression that can fully show the information of sample data by setting different quantiles,but also has its own superiority compared with quantile regression and expectile regression,due to its explicit expression and conservativeness in estimating.Here,we propose a linear extremile regression model and introduce a variable selection method using a penalty called a quasi elastic net(QEN)to solve high-dimensional problems.Moreover,we propose an EM algorithm and establish corresponding theoretical properties under some mild conditions.In numerical studies,we compare the QEN penalty with the,L_(0),L_(1),L_(2) and elastic net penalties,and the results show that the proposed method is effective and has certain advantages in analysis.