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Outlier detection and robust variable selection via the penalized weighted LAD-LASSO method |
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| Authors: | Yunlu Jiang Yan Wang Jiantao Zhang Baojian Xie Jibiao Liao Wenhui Liao |
| Institution: | aDepartment of Statistics, College of Economics, Jinan University, Guangzhou, People''s Republic of China;bCollege of Economics, Jinan University, Guangzhou, People''s Republic of China;cOffice of Educational Administration, Dongguan Open University, Dongguan, People''s Republic of China;dSchool of Financial Mathematics and Statistics, Guangdong University of Finance, Guangzhou, People''s Republic of China |
| Abstract: | This paper studies the outlier detection and robust variable selection problem in the linear regression model. The penalized weighted least absolute deviation (PWLAD) regression estimation method and the adaptive least absolute shrinkage and selection operator (LASSO) are combined to simultaneously achieve outlier detection, and robust variable selection. An iterative algorithm is proposed to solve the proposed optimization problem. Monte Carlo studies are evaluated the finite-sample performance of the proposed methods. The results indicate that the finite sample performance of the proposed methods performs better than that of the existing methods when there are leverage points or outliers in the response variable or explanatory variables. Finally, we apply the proposed methodology to analyze two real datasets. |
| Keywords: | Outlier detection robust regression penalized weighted least absolute deviation LASSO variable selection |