The task of analyzing extreme events with censoring effects is considered under a framework allowing for random covariate information. A wide class of estimators that can be cast as product-limit integrals is considered, for when the conditional distributions belong to the Frechet max-domain of attraction. The main mathematical contribution is establishing uniform conditions on the families of the regularly varying tails for which the asymptotic behaviour of the resulting estimators is tractable. In particular, a decomposition of the integral estimators in terms of exchangeable sums is provided, which leads to a law of large numbers and several central limit theorems. Subsequently, the finite-sample behaviour of the estimators is explored through a simulation study, and through the analysis of two real-life datasets. In particular, the inclusion of covariates makes the model significantly versatile and, as a consequence, practically relevant.

翻译：本文在允许随机协变量信息的框架下，研究了存在删失效应的极值事件分析任务。针对条件分布属于Frechet极大值吸引域的情形，考察了一类可表示为乘积限积分的宽泛估计量族。主要数学贡献在于建立了正则变化尾分布族的一致条件，使得所得估计量的渐近行为可解析处理。特别地，本文通过可交换和分解给出了积分估计量的表达式，由此推导出大数定律及若干中心极限定理。随后通过模拟研究和两个实际数据集分析，探究了估计量的有限样本性质。特别指出，协变量的引入使模型具有显著灵活性，从而提升了实际应用价值。