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 amount 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 prediction. Cantoni and Ronchetti (2001) proposed a robust frequentist approach which is now the most commonly applied. It consists in an estimator which is derived from a modification of the derivative of the log-likelihood. We propose an 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. We show that the approach possesses appealing theoretical and empirical properties. In particular, we show through a simulation study that it offers an advantage in terms of estimation performance.

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，伽马变体被用于对保险索赔金额进行建模。GLMs的一个缺陷是对异常值（即错误或极端数据点）缺乏稳健性。因此，数据主体部分与异常值之间的趋势差异会导致有偏的推断和预测。Cantoni 与 Ronchetti（2001）提出了一种稳健的频率学派方法，该方法目前应用最为广泛。该方法基于对数似然导数的修正推导出一个估计量。我们提出了一种基于建模的方法，其本质上有所不同。该方法能够对建模过程进行理解和解释，并且适用于频率学派和贝叶斯统计分析。我们证明该方法具有吸引人的理论和实证性质。特别地，通过模拟研究，我们表明其在估计性能方面具有优势。