  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.
