Robust regression against heavy heterogeneous contamination
Robust regression against heavy heterogeneous contamination
复制标题
针对严重异质污染的稳健回归
DOI：
10.1007/s00184-022-00874-1
复制
发表时间：
2022
期刊：
影响因子：
0.7
通讯作者：
Fujisawa Hironori
中科院分区：
文献类型：
--
作者：
Kawashima Takayuki;Fujisawa Hironori
该分歧是众所周知的，具有强大的鲁棒性，对重污染。凭借这一性质，已经提出了许多通过发散的应用。回归问题有两种类型的发散，其中基本度量的处理方式不同。在这项研究中，这两个分歧进行了比较，并发现它们之间的差异很大的异质污染，其中的离群值比例取决于解释变量。单偏差算法即使在非均匀污染下也具有很强的鲁棒性。另一个一般没有;然而，它具有均匀污染，其中离群值比率不依赖于解释变量，或者当响应变量的参数模型属于位置-尺度家族时，其中尺度不依赖于解释变量。Hung等人（Biometrics 74（1）：145-154，2018）讨论了逻辑回归模型的强鲁棒性，并额外假设调整参数足够大。在这项研究中获得的结果适用于任何参数模型，没有这样一个额外的假设。
The-divergence is well-known for having strong robustness against heavy contamination. By virtue of this property, many applications via the-divergence have been proposed. There are two types of-divergence for the regression problem, in which the base measures are handled differently. In this study, these two-divergences are compared, and a large difference is found between them under heterogeneous contamination, where the outlier ratio depends on the explanatory variable. One-divergence has the strong robustness even under heterogeneous contamination. The other does not have in general; however, it has under homogeneous contamination, where the outlier ratio does not depend on the explanatory variable, or when the parametric model of the response variable belongs to a location-scale family in which the scale does not depend on the explanatory variables. Hung et al. (Biometrics 74(1):145–154, 2018) discussed the strong robustness in a logistic regression model with an additional assumption that the tuning parameteris sufficiently large. The results obtained in this study hold foranyparametric modelwithoutsuch an additional assumption.