论文标题
强大的确定独立性筛选非多功能尺寸概括性线性模型
Robust Sure Independence Screening for Non-polynomial dimensional Generalized Linear Models
论文作者
论文摘要
我们考虑了非多功能顺序的超高维线性模型（GLM）中可变筛选的问题。由于在存在污染和噪声的情况下，流行的SIS方法非常不稳定，因此我们讨论了基于边缘回归系数的最小密度差异估计器（MDPDE）的新的可靠筛选程序。我们提出的筛选程序在纯净和受污染的数据情景下表现良好。我们为使用边缘MDPDE的人群以及样本方面的可变筛查提供了理论动机。特别是，我们证明边缘MDPDE是统一的一致性，导致我们提出的算法的肯定筛选特性。最后，我们提出了一个基于适当的MDPDE扩展名，用于在GLM中进行鲁棒的条件筛选，以及其确定筛选属性的推导。我们提出的方法通过广泛的数值研究以及有趣的真实数据应用来说明。
We consider the problem of variable screening in ultra-high dimensional generalized linear models (GLMs) of non-polynomial orders. Since the popular SIS approach is extremely unstable in the presence of contamination and noise, we discuss a new robust screening procedure based on the minimum density power divergence estimator (MDPDE) of the marginal regression coefficients. Our proposed screening procedure performs well under pure and contaminated data scenarios. We provide a theoretical motivation for the use of marginal MDPDEs for variable screening from both population as well as sample aspects; in particular, we prove that the marginal MDPDEs are uniformly consistent leading to the sure screening property of our proposed algorithm. Finally, we propose an appropriate MDPDE based extension for robust conditional screening in GLMs along with the derivation of its sure screening property. Our proposed methods are illustrated through extensive numerical studies along with an interesting real data application.
