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.

翻译：本文提出了一种新颖且全面的方法论，旨在应对随机删失背景下极端值带来的挑战。主要关注基于归一化上阶统计量的乘积限估计量的积分分析，即称为极端Kaplan-Meier积分。这些积分能够清晰地推导出多种重要的渐近分布性质，为传统的插件估计方法提供了替代方案。值得注意的是，该方法在最大吸引域中展现出稳健性和广泛适用性。一个引人注目的副产品是将广义Hill型极端值估计器扩展到覆盖所有最大吸引域，这本身具有独立的研究价值。