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：当拥有完整的原始损失严重度样本数据集时，存在众多替代最大似然估计（MLE）的稳健估计方法。然而，在处理分组损失严重度数据时，替代MLE的稳健方法选择非常有限，仅剩最小二乘法、最小Hellinger距离法和最优有界影响函数等少数方法。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帕累托分布的尾指数。通过应用中心极限定理建立MTuM的推断理论基础，并通过全面的模拟研究加以验证。