Multivariate Nonparametric Estimation of the Pickands Dependence Function using Bernstein Polynomials
Abstract
Many applications in risk analysis, especially in environmental sciences, require the estimation of the dependence among multivariate maxima. A way to do this is by inferring the Pickands dependence function of the underlying extreme-value copula. A nonparametric estimator is constructed as the sample equivalent of a multivariate extension of the madogram. Shape constraints on the family of Pickands dependence functions are taken into account by means of a representation in terms of a specific type of Bernstein polynomials. The large-sample theory of the estimator is developed and its finite-sample performance is evaluated with a simulation study. The approach is illustrated by analyzing clusters consisting of seven weather stations that have recorded weekly maxima of hourly rainfall in France from 1993 to 2011.
Cite
@article{arxiv.1405.5228,
title = {Multivariate Nonparametric Estimation of the Pickands Dependence Function using Bernstein Polynomials},
author = {G. Marcon and S. A. Padoan and P. Naveau and P. Muliere and J. Segers},
journal= {arXiv preprint arXiv:1405.5228},
year = {2016}
}