Abstract We describe a computational method for parameter estimation in linear regression, that is capable of simultaneously producing sparse estimates and dealing with outliers and heavy-tailed error distributions. The method used is based on the image restoration method proposed in [G. Huang, A. Lanza, S. Morigi, L. Reichel, and F. Sgallari, Majorization-minimization generalized Krylov subspace methods for l p - l q optimization applied to image restoration, BIT Numer. Math., 57 (2017), pp. 351–378]. It can be applied to problems of arbitrary size. The choice of certain parameters is discussed. Results obtained for simulated and real data are presented.

中文翻译：

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具有非凸损失和惩罚的大规模回归

摘要 我们描述了一种用于线性回归中参数估计的计算方法，该方法能够同时产生稀疏估计并处理异常值和重尾误差分布。所使用的方法基于[G. Huang、A. Lanza、S. Morigi、L. Reichel 和 F. Sgallari，用于图像恢复的 lp-lq 优化的 Majorization-minimization 广义 Krylov 子空间方法，BIT Numer。数学，57 (2017)，第 351–378 页]。它可以应用于任意大小的问题。讨论了某些参数的选择。给出了模拟和真实数据的结果。