Dependence Properties of Multivariate Max-Stable Distributions

TL;DR

This paper explores the dependence structure of multivariate max-stable distributions, generalizes existing inequalities, and develops improved nonparametric estimators that incorporate new dependence constraints.

Contribution

It extends inequalities for extremal coefficients, constructs bounds for higher order exponent measures, and introduces constrained estimators for better dependence modeling.

Findings

Derived new bounds for exponent measures consistent with lower-dimensional margins.

Proposed likelihood-based estimators that enforce dependence constraints.

Showed improved estimation accuracy over unconstrained methods.

Abstract

For an m-dimensional multivariate extreme value distribution there exist 2^{m}-1 exponent measures which are linked and completely characterise the dependence of the distribution and all of its lower dimensional margins. In this paper we generalise the inequalities of Schlather and Tawn (2002) for the sets of extremal coefficients and construct bounds that higher order exponent measures need to satisfy to be consistent with lower order exponent measures. Subsequently we construct nonparametric estimators of the exponent measures which impose, through a likelihood-based procedure, the new dependence constraints and provide an improvement on the unconstrained estimators.