A Euclidean likelihood estimator for bivariate tail dependence

TL;DR

This paper introduces a simple Euclidean likelihood estimator for the spectral measure in multivariate extreme value analysis, which is easy to compute, theoretically sound, and performs well in practice.

Contribution

The paper proposes a new Euclidean likelihood-based estimator for the spectral measure that is explicit, avoids Lagrange multipliers, and matches the limit distribution of existing maximum empirical likelihood estimators.

Findings

Estimator has the same limit distribution as the maximum empirical likelihood estimator.

Numerical experiments show good performance and identical behavior to existing methods.

Method successfully applied to analyze extreme temperature data.

Abstract

The spectral measure plays a key role in the statistical modeling of multivariate extremes. Estimation of the spectral measure is a complex issue, given the need to obey a certain moment condition. We propose a Euclidean likelihood-based estimator for the spectral measure which is simple and explicitly defined, with its expression being free of Lagrange multipliers. Our estimator is shown to have the same limit distribution as the maximum empirical likelihood estimator of J. H. J. Einmahl and J. Segers, Annals of Statistics 37(5B), 2953--2989 (2009). Numerical experiments suggest an overall good performance and identical behavior to the maximum empirical likelihood estimator. We illustrate the method in an extreme temperature data analysis.