Penalized M-Estimation Based on Standard Error Adjusted Adaptive Elastic-Net  

作　　者：WU Xianjun WANG Mingqiu HU Wenting TIAN Guo-Liang LI Tao 

机构地区：[1]School of Statistics and Mathematics,Zhongnan University of Economics and Law,Wuhan 430073,China [2]School of Statistics and Data Scicence,Qufu Normal University,Qufu 273165,China [3]Department of Statistics and Data Science,Southern University of Science and Technology,Shenzhen 518055,China

出　　处：《Journal of Systems Science & Complexity》2023年第3期1265-1284,共20页系统科学与复杂性学报（英文版）

基　　金：supported by the National Natural Science Foundation of China under Grant Nos.12271294,12171225 and 12071248.

摘　　要：When there are outliers or heavy-tailed distributions in the data, the traditional least squares with penalty function is no longer applicable. In addition, with the rapid development of science and technology, a lot of data, enjoying high dimension, strong correlation and redundancy, has been generated in real life. So it is necessary to find an effective variable selection method for dealing with collinearity based on the robust method. This paper proposes a penalized M-estimation method based on standard error adjusted adaptive elastic-net, which uses M-estimators and the corresponding standard errors as weights. The consistency and asymptotic normality of this method are proved theoretically. For the regularization in high-dimensional space, the authors use the multi-step adaptive elastic-net to reduce the dimension to a relatively large scale which is less than the sample size, and then use the proposed method to select variables and estimate parameters. Finally, the authors carry out simulation studies and two real data analysis to examine the finite sample performance of the proposed method. The results show that the proposed method has some advantages over other commonly used methods.

关 键 词：Adaptive elastic net -estimation oracle property standard error 

分 类 号：O212.1[理学—概率论与数理统计]