论文标题
基于稀疏高维线性回归模型的Rényi的伪差基于正规化方法
On regularization methods based on Rényi's pseudodistances for sparse high-dimensional linear regression models
论文作者
论文摘要
在过去的十年中，对于稀疏的高维线性回归模型，已经考虑了几种正则化方法，但是最常见的方法使用最小的（二次）或似然损失，因此对数据污染并不强大。一些作者通过根据差异度量（例如，密度功率差异，γ-差异等）而不是二次损失来考虑合适的损失函数来克服非舒适性问题。在本文中，我们将根据Rényi的伪抗解，共同考虑具有非符号惩罚的损失函数，以同时执行可变选择，并在非polynomial尺寸的高维线性回归模型中获得可变的参数估计器。我们提出的方法的所需甲骨文属性是从理论上得出的，其实用性是通过模拟和真实数据示例在数值上插入的。
Several regularization methods have been considered over the last decade for sparse high-dimensional linear regression models, but the most common ones use the least square (quadratic) or likelihood loss and hence are not robust against data contamination. Some authors have overcome the problem of non-robustness by considering suitable loss function based on divergence measures (e.g., density power divergence, gamma-divergence, etc.) instead of the quadratic loss. In this paper we shall consider a loss function based on the Rényi's pseudodistance jointly with non-concave penalties in order to simultaneously perform variable selection and get robust estimators of the parameters in a high-dimensional linear regression model of non-polynomial dimensionality. The desired oracle properties of our proposed method are derived theoretically and its usefulness is illustustrated numerically through simulations and real data examples.
