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Degrees of freedom for regularized regression with Huber loss and linear constraints

Author

Listed:
  • Yongxin Liu

    (Nanjing Audit University)

  • Peng Zeng

    (Auburn University)

  • Lu Lin

    (Shandong Technology and Business University
    Qufu Normal University)

Abstract

The ordinary least squares estimate for linear regression is sensitive to errors with large variance. It is not robust to heavy-tailed errors or outliers, which are commonly encountered in applications. In this paper, we propose to use a Huber loss function with a generalized penalty to achieve robustness in estimation and variable selection. The performance of estimation and variable selection can be further improved by incorporating any prior knowledge as constraints on parameters. A formula of degrees of freedom of the fit is derived, which is utilized in information criteria for model selection. Simulation studies and real examples are used to demonstrate the application of degrees of freedom and the performance of the model selection methods.

Suggested Citation

  • Yongxin Liu & Peng Zeng & Lu Lin, 2021. "Degrees of freedom for regularized regression with Huber loss and linear constraints," Statistical Papers, Springer, vol. 62(5), pages 2383-2405, October.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:5:d:10.1007_s00362-020-01192-2
    DOI: 10.1007/s00362-020-01192-2
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