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

Wu，Xianjun1,2; Wang，Mingqiu2; Hu，Wenting2; Tian，Guo Liang3; Li，Tao3

2023-06-01

10.1007/s11424-023-1400-0

Journal of Systems Science and Complexity   影响因子和分区

1009-6124

1559-7067

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there are outliers or heavy-tailed distributions in the data, the traditional least squares with penalty function is no longer applicable.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.

Adaptive elastic net M-estimation oracle property standard error

SCI ; EI

英语

其他

National Natural Science Foundation of China["12271294","12171225","12071248"]

Mathematics

Mathematics, Interdisciplinary Applications

WOS:000993069200018

SPRINGER HEIDELBERG

20232214152660

Sampling

2-s2.0-85160014842

Scopus

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

Wu，Xianjun,Wang，Mingqiu,Hu，Wenting,et al. Penalized M-Estimation Based on Standard Error Adjusted Adaptive Elastic-Net[J]. Journal of Systems Science and Complexity,2023,36(3):1265-1284.

Wu，Xianjun,Wang，Mingqiu,Hu，Wenting,Tian，Guo Liang,&Li，Tao.(2023).Penalized M-Estimation Based on Standard Error Adjusted Adaptive Elastic-Net.Journal of Systems Science and Complexity,36(3),1265-1284.

Wu，Xianjun,et al."Penalized M-Estimation Based on Standard Error Adjusted Adaptive Elastic-Net".Journal of Systems Science and Complexity 36.3(2023):1265-1284.