On the estimation of the extreme value index for randomly right-truncated data and application

TL;DR

This paper proposes a new consistent estimator for the extreme value index in the context of randomly right-truncated data, demonstrating its asymptotic properties and finite sample performance, with applications to reinsurance premium estimation.

Contribution

It introduces a novel estimator for the extreme value index under random truncation and establishes its asymptotic normality using a weighted tail-copula process framework.

Findings

Estimator is consistent and asymptotically normal.

Finite sample behavior confirmed through simulations.

Application to reinsurance premium estimation demonstrated.

Abstract

We introduce a consistent estimator of the extreme value index under random truncation based on a single sample fraction of top observations from truncated and truncation data. We establish the asymptotic normality of the proposed estimator by making use of the weighted tail-copula process framework and we check its finite sample behavior through some simulations. As an application, we provide asymptotic normality results for an estimator of the excess-of-loss reinsurance premium.