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 a 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), pecifically designed to estimate the tail index of a Pareto distribution from grouped data. Inferential justification of the MTuM is established by employing the central limit theorem and validating it through a comprehensive simulation study.

中文翻译：

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基于分组数据的单参数帕累托分布尾部指数的鲁棒估计

当完全观察到的基础损失严重性样本数据集可用时，存在许多稳健的估计器作为最大似然估计器（MLE）的替代品。然而，在处理分组损失严重性数据时，MLE 的稳健替代方案的选择变得非常有限，只有少数方法可用，例如最小二乘法、最小海林格距离和最优有界影响函数。本文介绍了一种新颖的鲁棒估计技术，即截断矩方法 (MTuM)，专门用于根据分组数据估计 Pareto 分布的尾部指数。MTuM 的推理论证是通过采用中心极限定理建立的，并通过全面的模拟研究对其进行验证。