Semiparametric bivariate extreme-value copulas

TL;DR

This paper introduces a new semiparametric method for modeling bivariate extreme-value copulas, combining transformations and spline techniques to efficiently estimate complex dependence structures, demonstrated on simulated and real data including gravitational wave observations.

Contribution

It presents a novel semiparametric approach for bivariate extreme-value copulas using transformations and splines, enabling efficient maximum likelihood estimation without restrictive constraints.

Findings

Outperforms existing nonparametric methods on small and medium samples.

Effectively captures complex dependence structures in simulated data.

Successfully applied to gravitational wave data from LIGO and Virgo.

Abstract

Extreme-value copulas arise as the limiting dependence structure of component-wise maxima. Defined in terms of a functional parameter, they are one of the most widespread copula families due to their flexibility and ability to capture asymmetry. Despite this, meeting the complex analytical properties of this parameter in an unconstrained setting remains a challenge, restricting most uses to models with very few parameters or nonparametric models. Focusing on the bivariate case, we propose a novel semiparametric approach. Our procedure relies on a series of transformations, including Williamson's transform and starting from a zero-integral spline. Without further constraints, wholly compliant solutions can be efficiently obtained through maximum likelihood estimation, leveraging gradient optimization. We successfully conducted several experiments on simulated and real-world data. Our method outperforms another well-known nonparametric technique over small and medium-sized samples in various settings. Its expressiveness is illustrated with precious data gathered by the gravitational wave detection LIGO and Virgo collaborations.