基于调整秩回归的组变量选择  

Group selection based on adjusted regularized rank regression

作　　者：王萧博 吴贤君 王明秋[2] WANG Xiaobo;WU Xianjun;WANG Mingqiu(School of Economics and Management,Zaozhuang University,277160,Zaozhuang;School of Statistics and Data Science,Qufu Normal University,273165,Qufu,Shandong,PRC)

机构地区：[1]枣庄学院经济与管理学院,枣庄市277160 [2]曲阜师范大学统计与数据科学学院,山东省曲阜市273165

出　　处：《曲阜师范大学学报（自然科学版）》2022年第2期11-18,F0002,共9页Journal of Qufu Normal University(Natural Science)

基　　金：山东省自然科学基金(ZR2019MA002).

摘　　要：EXP惩罚是一种指数形式的惩罚函数,它近似于L_(0)惩罚. EXP惩罚最小二乘估计具有模型选择的相合性和渐近正态性.但是,惩罚最小二乘方法对重尾分布和含有异常值的混合分布的效果并不理想.该文考虑回归模型中的变量是以组结构形式存在的,研究基于调整秩回归的EXP型组变量选择,给出了调整秩回归估计的理论性质,并通过数据模拟和实例分析,检验调整秩回归的EXP惩罚的效果,结果表明这种方法具有较好的表现.The EXP penalty is an exponential type penalty which very closely resembles the L_(0)penalty. The EXP penalized least squares estimators are showed to have selection consistency and the asymptotic normality. However, the efficiency of least squares based penalization is adversely affected by outliers and heavy tailed distributions. This paper considers regression problems in which the covariates can be grouped. The interest is in studying the adjusted regularized rank regression based on the EXP penalty for group selection. This paper discusses some theoretical properties of adjusted rank regression estimator and provides theoretical results with simulation studies and a real data analysis. The results show that the method performs well.

关 键 词：变量选择 EXP惩罚 调整秩回归 组变量 Oracle性质 

分 类 号：O212[理学—概率论与数理统计]