Heterogeneous extremes in the presence of random covariates and censoring

TL;DR

This paper develops a theoretical framework for analyzing extreme events with censoring and covariates, establishing asymptotic properties of estimators and demonstrating their practical relevance through simulations and real data.

Contribution

It introduces uniform conditions on tail behaviors for product-limit estimators in the presence of covariates and censoring, with new asymptotic results and practical insights.

Findings

Establishes law of large numbers and CLTs for estimators

Demonstrates estimator performance via simulations

Analyzes real datasets showing model versatility

Abstract

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.