The adaptive BerHu penalty in robust regression
The adaptive BerHu penalty in robust regression
复制标题
鲁棒回归中的自适应 BerHu 惩罚
DOI：
10.1080/10485252.2016.1190359
复制
发表时间：
2016
影响因子：
1.2
通讯作者：
Laurent Zwald
中科院分区：
文献类型：
--
作者：
S. Lambert;Laurent Zwald
我们打算结合联合收割机胡贝尔的损失与自适应反向版本作为惩罚函数。目的是双重的：首先，我们想提出一个估计，是强大的数据受到重尾误差或离群值。其次，我们希望克服高度相关的预测变量存在的变量选择问题。例如，在这个框架中，自适应最小绝对收缩和选择算子（lasso）不是非常令人满意的变量选择方法，尽管它是用于同时估计和变量选择的流行技术。我们称这种新的惩罚为自适应BerHu惩罚。至于弹性净惩罚，小系数通过其范数对该惩罚做出贡献，而较大的系数导致其二次增长（如岭回归）。我们将表明，估计与Huber损失相结合的自适应BerHu罚款享有理论性质在固定的设计背景下。这种方法相比，现有的正则化方法，如自适应弹性网，并通过模拟研究和真实的数据说明。
We intend to combine Huber's loss with an adaptive reversed version as a penalty function. The purpose is twofold: first we would like to propose an estimator that is robust to data subject to heavy-tailed errors or outliers. Second we hope to overcome the variable selection problem in the presence of highly correlated predictors. For instance, in this framework, the adaptive least absolute shrinkage and selection operator (lasso) is not a very satisfactory variable selection method, although it is a popular technique for simultaneous estimation and variable selection. We call this new penalty the adaptive BerHu penalty. As for elastic net penalty, small coefficients contribute through their norm to this penalty while larger coefficients cause it to grow quadratically (as ridge regression). We will show that the estimator associated with Huber's loss combined with the adaptive BerHu penalty enjoys theoretical properties in the fixed design context. This approach is compared to existing regularisation methods such as adaptive elastic net and is illustrated via simulation studies and real data.
影响因子：
2.7
作者：
Wang, Hansheng;Li, Runze;Tsai, Chih-Ling
通讯作者：
Tsai, Chih-Ling
影响因子：
4.5
作者：
Zou H;Zhang HH
通讯作者：
Zhang HH