Non Linear Models for Extremal Dependence

Abstract

The dependence structure of max-stable random vectors can be characterized by its Pickands dependence function. In many applications the extremal dependence measure varies with covariates. We develop a new flexible semi-parametric method for the estimation of non-stationary multivariate Pickands dependence functions. The proposed construction is based on an accurate max-projection allowing to pass from the multivariate to the univariate setting and to rely on the generalized additive modelling framework. In the bivariate case, the resulting estimator of the Pickands function is regularized using constrained median smoothing B-splines and bootstrap confidence intervals are constructed. In higher dimensions, an extension is proposed. We present the results from a simulation study and apply the new methodology to a real dataset.