The \(\gamma \)-divergence is well-known for having strong robustness against heavy contamination. By virtue of this property, many applications via the \(\gamma \)-divergence have been proposed. There are two types of \(\gamma \)-divergence for the regression problem, in which the base measures are handled differently. In this study, these two \(\gamma \)-divergences are compared, and a large difference is found between them under heterogeneous contamination, where the outlier ratio depends on the explanatory variable. One \(\gamma \)-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 parameter \(\gamma \) is sufficiently large. The results obtained in this study hold for any parametric model without such an additional assumption.

\(\gamma \) -散度以对重污染具有很强的鲁棒性而闻名。凭借这一性质，已经提出了许多通过\(\gamma \) -divergence 的应用。回归问题有两种类型的\(\gamma \) -散度，其中基本度量的处理方式不同。本研究对这两个\(\gamma\) -分歧进行了比较，发现在异质污染下它们之间存在很大差异，其中离群值比取决于解释变量。一\(\伽马\)-divergence 即使在异质污染下也具有很强的鲁棒性。其他一般没有；但是，它具有均质污染，其中异常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尺度不依赖于解释变量的位置尺度族时。洪等人。(Biometrics 74(1):145–154, 2018) 讨论了逻辑回归模型中的强稳健性，并附加假设调整参数\(\gamma \)足够大。本研究中获得的结果适用于任何没有这种额外假设的 参数模型。