Penalized M-Estimation Based on Standard Error Adjusted Adaptive Elastic-Net
作者机构：School of Statistics and MathematicsZhongnan University of Economics and LawWuhan 430073China School of Statistics and Data ScicenceQufu Normal UniversityQufu 273165China Department of Statistics and Data ScienceSouthern University of Science and TechnologyShenzhen 518055China
出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)
年 卷 期：2023年第36卷第3期
页 面：1265-1284页
核心收录：
学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学]
基 金：supported by the National Natural Science Foundation of China under Grant Nos.12271294 12171225 and 12071248
主 题：Adaptive elastic net -estimation oracle property standard error
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there are outliers or heavy-tailed distributions in the data, the traditional least squares with penalty function is no longer applicable.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.
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