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.

中文翻译：

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具有 Huber 损失和线性约束的正则化回归的自由度

线性回归的普通最小二乘估计对大方差的误差很敏感。它对应用程序中常见的重尾错误或异常值不稳健。在本文中，我们建议使用带有广义惩罚的 Huber 损失函数来实现估计和变量选择的鲁棒性。通过将任何先验知识作为参数约束，可以进一步提高估计和变量选择的性能。推导出拟合的自由度公式，该公式用于模型选择的信息标准。仿真研究和实际示例用于演示自由度的应用和模型选择方法的性能。