Robust heavy-tailed versions of generalized linear models with applications in actuarial science
针对广义线性模型对异常值不稳健的问题，提出一种基于建模的替代方法，适用于频率学派和贝叶斯分析，具有优良的理论和实证性质，可用于保险索赔金额建模。
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. The objective is to propose an alternative approach which is modelling-based and thus fundamentally different. Such an approach allows for an understanding and interpretation of the modelling, and it can be applied for both frequentist and Bayesian statistical analyses. The proposed approach possesses appealing theoretical and empirical properties.