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：当拥有完全观测的底层损失严重性样本数据集时，存在大量稳健估计量作为最大似然估计（MLE）的替代方案。然而，在处理分组损失严重性数据时，MLE的稳健替代方法的选择变得非常有限，仅有少数几种方法可用，例如最小二乘法、最小Hellinger距离法和最优有界影响函数法。本文介绍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并借助全面的仿真研究进行验证，确立了MTuM的推断合理性。