Numerous robust estimators exist as alternatives to the maximum likelihood estimator (MLE) when a completely observed ground-up loss severity sample dataset is available. However, the options for robust alternatives to MLE become significantly limited when dealing with grouped loss severity data, with only a handful of methods like least squares, minimum Hellinger distance, and optimal bounded influence function available. This paper introduces a novel robust estimation technique, the Method of Truncated Moments (MTuM), specifically designed to estimate the tail index of a Pareto distribution from grouped data. Inferential justification of MTuM is established by employing the central limit theorem and validating them through a comprehensive simulation study.

翻译：当存在完全观测的原始损失严重度样本数据集时，存在众多稳健估计量作为极大似然估计（MLE）的替代方案。然而，在处理分组损失严重度数据时，MLE的稳健替代选择显著受限，仅剩少数方法如最小二乘法、最小Hellinger距离法和最优有界影响函数法可用。本文提出了一种新颖的稳健估计技术——截断矩法（MTuM），专门用于从分组数据中估计Pareto分布的尾部指数。通过应用中心极限定理建立MTuM的推断合理性，并借助全面的模拟研究加以验证。