# Extreme value statistics for censored data with heavy tails under competing risks

## TL;DR

This paper introduces a novel estimator for the extreme value index in censored data with competing risks, demonstrating its asymptotic normality and finite-sample performance through simulations.

## Contribution

It proposes the first estimator based on an Aalen-Johansen integral for extreme value index in this context, addressing heavy tails and censoring.

## Key findings

- Estimator is asymptotically normal.
- Performs well in finite-sample simulations.
- Enables estimation of extreme quantiles in competing risks.

## Abstract

This paper addresses the problem of estimating, in the presence of random censoring as well as competing risks, the extreme value index of the (sub)-distribution function associated to one particular cause, in the heavy-tail case. Asymptotic normality of the proposed estimator (which has the form of an Aalen-Johansen integral, and is the first estimator proposed in this context) is established. A small simulation study exhibits its performances for finite samples. Estimation of extreme quantiles of the cumulative incidence function is also addressed.