The challenge of using small sample sizes for operational risk capital models fitted via maximum likelihood estimation is well recognized, yet the literature generally provides warning examples rather than a systematic approach. We present a general framework for analyzing maximum likelihood estimation error on operational value-at-risk as a function of sample size for five severity distributions commonly used in operational risk capital models. More specifically, we study the estimation error along three dimensions: the choice of severity distribution, the sample size and the heaviness of the underlying losses. We apply these results to model selection and explore implications for operational risk modeling.

中文翻译：

---

最大似然估计误差和运营风险价值稳定性

对通过最大似然估计拟合的操作风险资本模型使用小样本量的挑战是众所周知的，但文献通常提供警告示例而不是系统方法。我们提出了一个通用框架，用于分析作为操作风险资本模型中常用的五种严重性分布的样本大小的函数的操作风险价值的最大似然估计误差。更具体地说，我们从三个维度研究估计误差：严重性分布的选择、样本大小和潜在损失的严重程度。我们将这些结果应用于模型选择并探索对操作风险建模的影响。