Jiang Yunlu, Wang Yan, Zhang Jiantao, Xie Baojian, Liao Jibiao, Liao Wenhui
Department of Statistics, College of Economics, Jinan University, Guangzhou, People's Republic of China.
College of Economics, Jinan University, Guangzhou, People's Republic of China.
J Appl Stat. 2020 Feb 4;48(2):234-246. doi: 10.1080/02664763.2020.1722079. eCollection 2021.
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.
本文研究线性回归模型中的异常值检测和稳健变量选择问题。将惩罚加权最小绝对偏差（PWLAD）回归估计方法与自适应最小绝对收缩和选择算子（LASSO）相结合，以同时实现异常值检测和稳健变量选择。提出了一种迭代算法来解决所提出的优化问题。通过蒙特卡罗研究评估了所提方法的有限样本性能。结果表明，当响应变量或解释变量中存在杠杆点或异常值时，所提方法的有限样本性能优于现有方法。最后，我们应用所提方法对两个真实数据集进行分析。
