A novel and comprehensive methodology designed to tackle the challenges posed by extreme values in the context of random censorship is introduced. The main focus is on the analysis of integrals based on the product-limit estimator of normalized upper order statistics, called extreme Kaplan--Meier integrals. These integrals allow for the transparent derivation of various important asymptotic distributional properties, offering an alternative approach to conventional plug-in estimation methods. Notably, this methodology demonstrates robustness and wide applicability within the scope of max-domains of attraction. A noteworthy by-product is the extension of generalized Hill-type estimators of extremes to encompass all max-domains of attraction, which is of independent interest. The theoretical framework is applied to construct novel estimators for positive and real-valued extreme value indices for right-censored data. Simulation studies supporting the theory are provided.

翻译：本文提出了一种新颖且全面的方法论，旨在应对随机截尾背景下极值所带来的挑战。主要聚焦于基于归一化上阶统计量的乘积限估计量（称为极值Kaplan-Meier积分）的积分分析。这些积分能够透明地推导出各种重要的渐近分布性质，为传统的插件估计方法提供了一种替代途径。值得注意的是，该方法在最大吸引域范围内展现出鲁棒性和广泛的适用性。一个值得关注的副产品是将广义Hill型极值估计量扩展至涵盖所有最大吸引域，这本身具有独立的研究价值。该理论框架被应用于构建针对右截尾数据的正极值指数和实值极值指数的新型估计量。文中提供了支持该理论的模拟研究。