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，最大似然估计（MLE）有多种稳健估计方法作为替代。然而，在处理分组损失严重度数据时，MLE的稳健替代选项变得极为有限，仅有最小二乘法、最小赫林格距离法和最优有界影响函数法等少数方法可用。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估计帕累托分布的尾部指数。通过应用中心极限定理建立了MTuM的推断合理性，并借助全面的模拟研究进行了验证。