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

Yongxin Liu, Peng Zeng () and Lu Lin
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Yongxin Liu: Nanjing Audit University
Peng Zeng: Auburn University
Lu Lin: Shandong Technology and Business University

Statistical Papers, 2021, vol. 62, issue 5, No 15, 2383-2405

Abstract: 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.

Keywords: Degrees of freedom; Generalized lasso; Huber loss; KKT conditions; Linear constraints (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00362-020-01192-2

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