An M-estimator for tail dependence in arbitrary dimensions

TL;DR

This paper introduces a new M-estimator for tail dependence parameters in multivariate extreme value models, ensuring consistency and asymptotic normality, applicable to both discrete and continuous spectral measures.

Contribution

The paper proposes a novel M-estimator for tail dependence parameters that guarantees a unique solution and broad applicability to various spectral measures.

Findings

Estimator is consistent and asymptotically normal.

Method applies to both discrete and continuous spectral measures.

Examples show effective performance and applicability.

Abstract

Consider a random sample in the max-domain of attraction of a multivariate extreme value distribution such that the dependence structure of the attractor belongs to a parametric model. A new estimator for the unknown parameter is defined as the value that minimizes the distance between a vector of weighted integrals of the tail dependence function and their empirical counterparts. The minimization problem has, with probability tending to one, a unique, global solution. The estimator is consistent and asymptotically normal. The spectral measures of the tail dependence models to which the method applies can be discrete or continuous. Examples demonstrate the applicability and the performance of the method.