Generalized linear models (GLMs) form one of the most popular classes of models in statistics. The gamma variant is used, for instance, in actuarial science for the modelling of claim amounts in insurance. A flaw of GLMs is that they are not robust against outliers (i.e., against erroneous or extreme data points). A difference in trends in the bulk of the data and the outliers thus yields skewed inference and predictions. To address this problem, robust methods have been introduced. The most commonly applied robust method is frequentist and consists in an estimator which is derived from a modification of the derivative of the log-likelihood. We propose an alternative approach which is modelling-based and thus fundamentally different. It allows for an understanding and interpretation of the modelling, and it can be applied for both frequentist and Bayesian statistical analyses. The approach possesses appealing theoretical and empirical properties.

翻译：广义线性模型（GLMs）是统计学中最常用的模型类别之一。例如，在精算科学中，伽马变体被用于保险索赔金额的建模。GLMs的一个缺陷是它们对异常值（即错误或极端数据点）不具备鲁棒性。因此，数据主体与异常值之间的趋势差异会导致偏差的推断和预测。为解决此问题，人们引入了鲁棒方法。最常用的鲁棒方法是频率学派方法，其通过对数似然导数的修正推导出估计量。我们提出了一种基于建模的替代方法，该方法在本质上截然不同。它能够理解和解释建模过程，并可同时应用于频率学派和贝叶斯统计分析。该方法在理论和实证方面均具有吸引人的特性。