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 the analysis of integrals based on the product-limit estimator of normalized top-order statistics, denoted extreme Kaplan--Meier integrals. These integrals allow for 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. An additional noteworthy by-product is the extension of residual estimation 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顶端次序统计量的乘积限估计量的积分分析，即极端Kaplan-Meier积分。这些积分能够清晰推导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范围内展现出鲁棒性和广泛适用性。一个额外的重要附带成果是将极端值的残差估计扩展至涵盖所有最大吸引域，这本身具有独立的研究价值。