Multivariate Nonparametric Estimation of the Pickands Dependence Function using Bernstein Polynomials

Many applications in risk analysis, especially in environmental sciences, re-quire the estimation of the dependence among multivariate maxima. A way to do this is by inferring the so-called Pickands dependence function used in multivariate Extreme Value Theory. In this context, a clear advantage of a nonparametric approach over a parametric one is its flexibility and theoretical generality. Beyond the bivariate case, nonparametric estimation of the depen-dence function remains a challenging task and an active research field. In this article, we propose a new nonparametric approach for estimating the Pickands dependence function and we insure that it obeys all Pickands ’ constraints by taking advantage of a specific type of Bernstein polynomials representation. We discuss the properties of the proposed estimation method and illustrate its performance with a simulation study. For moderate dimension sizes, we illus-trate our approach by analyzing clusters made of seven weather stations that have recorded weekly maxima of hourly rainfall in France from 1996 to 2011