Outlier detection and robust variable selection via the penalized weighted LAD-LASSO method

• Published in: Journal of applied statistics Vol. 48; no. 2; pp. 234 - 246
• Main Authors: Jiang, Yunlu, Wang, Yan, Zhang, Jiantao, Xie, Baojian, Liao, Jibiao, Liao, Wenhui
• Format: Journal Article
• Language: English
• Published: England Taylor & Francis 25.01.2021; Taylor & Francis Ltd
• Subjects: Data analysis; Feature selection; Iterative algorithms; Iterative methods; LASSO; Monte Carlo simulation; Optimization; Outlier detection; Outliers (statistics); penalized weighted least absolute deviation; Performance evaluation; Regression analysis; Regression models; robust regression; Robustness (mathematics); Statistical methods; variable selection; robust regression; Outlier detection; variable selection; penalized weighted least absolute deviation; LASSO
• ISSN: 0266-4763; 1360-0532
• DOI: 10.1080/02664763.2020.1722079

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.