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

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Listed:
  • Yunlu Jiang
  • Yan Wang
  • Jiantao Zhang
  • Baojian Xie
  • Jibiao Liao
  • Wenhui Liao

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.

Suggested Citation

  • Yunlu Jiang & Yan Wang & Jiantao Zhang & Baojian Xie & Jibiao Liao & Wenhui Liao, 2021. "Outlier detection and robust variable selection via the penalized weighted LAD-LASSO method," Journal of Applied Statistics, Taylor & Francis Journals, vol. 48(2), pages 234-246, January.
    • Handle: RePEc:taf:japsta:v:48:y:2021:i:2:p:234-246
    DOI: 10.1080/02664763.2020.1722079
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    Cited by:

    1. Elyasiani, Elyas & Movaghari, Hadi, 2022. "Determinants of corporate cash holdings: An application of a robust variable selection technique," International Review of Economics & Finance, Elsevier, vol. 80(C), pages 967-993.
    2. Shengfei Tang & Yanmei Shi & Qi Zhang, 2023. "Bias-Corrected Inference of High-Dimensional Generalized Linear Models," Mathematics, MDPI, vol. 11(4), pages 1-14, February.
    3. Yafen Ye & Renyong Chi & Yuan-Hai Shao & Chun-Na Li & Xiangyu Hua, 2022. "Indicator Selection of Index Construction by Adaptive Lasso with a Generic $$\varepsilon $$ ε -Insensitive Loss," Computational Economics, Springer;Society for Computational Economics, vol. 60(3), pages 971-990, October.

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