Multivariate Tail Estimation: Conditioning on an extreme event

TL;DR

This paper develops a non-parametric approach for estimating characteristics of multivariate tail dependence conditioned on extreme events, introducing a quasi-spectral decomposition to enhance estimator efficiency.

Contribution

It proposes a novel quasi-spectral decomposition method for improved tail dependence estimation in multivariate extremes, supported by asymptotic theory and simulations.

Findings

Estimator efficiency is improved using the quasi-spectral decomposition.

Asymptotic normality is established for the proposed estimators.

Simulation studies confirm theoretical advantages.

Abstract

We consider regularly varying random vectors. Our goal is to estimate in a non-parametric way some characteristics related to conditioning on an extreme event, like the tail dependence coefficient. We introduce a quasi-spectral decomposition that allow to improve efficiency of estimators. Asymptotic normality of estimators is based on weak convergence of tail empirical processes. Theoretical results are supported by simulation studies.