Nonparametric estimation of the dependence among multivariate rainfall maxima

Abstract

Multivariate analysis of extreme values has an increasing range of applications in risk analysis, especially in the fields of environmental sciences. For example, it would be of interest for hydrologists to extract relevant information hidden in complex spatial-temporal rainfall datasets. The aim of this work is to analyse the dependence structures of weekly maxima of hourly rainfall in France recorded from 1993 to 2011. Some weather stations, initially organised in clusters, are analysed in order to summarise the dependence within all groups of seven stations. However, beyond the bivariate case, the analysis of the dependence structures for moderately high dimensional problems is still challenging. Estimation methods for assessing the extremal dependence must satisfy appropriate assumptions for guaranteeing valid results. The approach used here focuses on the nonparametric estimation of the Pickands dependence function through a specific type of Bernstein polynomial representation which ensures that all required constraints are verified.