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Robust Moderately Clipped LASSO for Simultaneous Outlier Detection and Variable Selection

Author

Listed:
  • Yang Peng

    (Department of Mathematics and Statistics University of North Carolina at Greensboro)

  • Bin Luo

    (Duke University)

  • Xiaoli Gao

    (Department of Mathematics and Statistics University of North Carolina at Greensboro)

Abstract

Outlier detection has become an important and challenging issue in high-dimensional data analysis due to the coexistence of data contamination and high-dimensionality. Most existing widely used penalized least squares methods are sensitive to outliers due to the l2 loss. In this paper, we proposed a Robust Moderately Clipped LASSO (RMCL) estimator, that performs simultaneous outlier detection, variable selection and robust estimation. The RMCL estimator can be efficiently solved using the coordinate descent algorithm in a convex-concave procedure. Our numerical studies demonstrate that the RMCL estimator possesses superiority in both variable selection and outlier detection and thus can be advantageous in difficult prediction problems with data contamination.

Suggested Citation

  • Yang Peng & Bin Luo & Xiaoli Gao, 2022. "Robust Moderately Clipped LASSO for Simultaneous Outlier Detection and Variable Selection," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 694-707, November.
    • Handle: RePEc:spr:sankhb:v:84:y:2022:i:2:d:10.1007_s13571-022-00279-0
    DOI: 10.1007/s13571-022-00279-0
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    References listed on IDEAS

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    6. Xueqin Wang & Yunlu Jiang & Mian Huang & Heping Zhang, 2013. "Robust Variable Selection With Exponential Squared Loss," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 632-643, June.
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