Semiparametric bivariate extreme-value copulas

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. In this paper, we focus on the bivariate case and propose a novel approach for estimating this functional parameter in a semiparametric manner. Our procedure relies on a series of transformations, including Williamson's transform and starting from a zero-integral spline. Spline coordinates are fit through maximum likelihood estimation, leveraging gradient optimization, without imposing further constraints. Our method produces efficient and wholly compliant solutions. We successfully conducted several experiments on both simulated and real-world data. Specifically, we test our method on scarce data gathered by the gravitational wave detection LIGO and Virgo collaborations.