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.
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