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 its flexibility and ability to capture asymmetry. Despite this, meeting the complex analytical properties of this parameter in an unconstrained setting still remains a challenge, restricting most uses to either models with very few parameters or non-parametric models. On 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 basic transformations starting from a zero-integral spline. Spline coordinates are fit through maximum likelihood estimation, leveraging gradient optimization, without imposing further constraints. We conduct several experiments on both simulated and real data. Specifically, we test our method on scarce data gathered by the gravitational wave detection LIGO and Virgo collaborations.