The classical credibility theory is a cornerstone of experience rating, especially in the field of property and casualty insurance. An obstacle to putting the credibility theory into practice is the conversion of available prior information into a precise choice of crucial hyperparameters. In most real-world applications, the information necessary to justify a precise choice is lacking, so we propose an imprecise credibility estimator that honestly acknowledges the imprecision in the hyperparameter specification. This results in an interval estimator that is doubly robust in the sense that it retains the credibility estimator’s freedom from model specification and fast asymptotic concentration, while simultaneously being insensitive to prior hyperparameter specification.

中文翻译：

---

不精确的可信度理论

经典可信度理论是经验评级的基石，尤其是在财产和意外伤害保险领域。将可信度理论付诸实践的一个障碍是将可用的先验信息转换为关键超参数的精确选择。在大多数实际应用中，缺乏证明精确选择所需的信息，因此我们提出了一个不精确的可信度估计器这诚实地承认了超参数规范中的不精确性。这导致一个区间估计器在某种意义上具有双重鲁棒性，即它保留了可信度估计器不受模型规范和快速渐近集中的影响，同时对先前的超参数规范不敏感。