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Robust penalized estimation via Welsch loss with group Lasso
Journal of the Korean Data & Information Science Society 2021;32:657-68
Published online May 31, 2021;
© 2021 Korean Data and Information Science Society.

Joonsung Kang1

1Department of Information Statistics, Gangneung-Wonju National University
Correspondence to: 1 Associate professor, Department of Information Statistics, Gangneung-Wonju national University, Jukheon-gil 7, Gangneung-si, 25457, Republic of Korea. E-mail:
Received March 2, 2021; Revised April 7, 2021; Accepted April 26, 2021.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Robust estimation is widely used for analyzing statistical inference. We investigate penalized robust estimation via Welsch loss function with group Lasso method in high- dimensional linear regression models with group structure in this paper. This penalty identifies the significant groups of predictor variables. Robust estimation with group Lasso has crucial meaning in that it accompanies the large p (the number of predictors) small n (sample size) problems.We present the updating algorithms for this group Lasso problem. Compared with other penalty functions, we carried out simulation studies in order to assess the performance of the proposed method and the real dataset was demonstrated numerically for illustration purpose.
Keywords : Robust estimator, Welsch, penalized regression, group-Lasso, Huber.