Likelihood estimators for multivariate extremes

TL;DR

This paper compares different likelihood estimators for multivariate extreme value models, clarifies their relationships, and evaluates their effectiveness in estimating extremal dependence and predicting future extremes using the logistic model.

Contribution

It provides a detailed analysis of the connections between main likelihood estimators for multivariate extremes and assesses their practical performance.

Findings

Likelihood estimators are interconnected and can be compared directly.

Estimators effectively capture extremal dependence in the logistic model.

Simulation results demonstrate estimator accuracy in predicting future extremes.

Abstract

The main approach to inference for multivariate extremes consists in approximating the joint upper tail of the observations by a parametric family arising in the limit for extreme events. The latter may be expressed in terms of componentwise maxima, high threshold exceedances or point processes, yielding different but related asymptotic characterizations and estimators. The present paper clarifies the connections between the main likelihood estimators, and assesses their practical performance. We investigate their ability to estimate the extremal dependence structure and to predict future extremes, using exact calculations and simulation, in the case of the logistic model.