Nonparametric estimation of the dependence among multivariate rainfall maxima G. Marcon 1,* , S.A. Padoan 1 , P. Naveau 2 and P. Muliere 1 1 Bocconi Universtity, Department of Decision Sciences, Milan, Italy; giulia.marcon@phd.unibocconi.it, simone.padoan@unibocconi.it, pietro.muliere@unibocconi.it 2 Laboratoire des Sciences du Climat et l’Environnement CNRS, Gif-sur-Yvette, France; Philippe.Naveau@lsce.ipsl.fr * Corresponding author 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 chal- lenging. Estimation methods for assessing the extremal dependence must satisfy appropriate assump- tions 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. Keywords. Extreme values; Rainfall maxima; Pickands dependence function; Nonparametric estima- tion; Bernstein polynomials. 1 Introduction To study the stochastic behaviour of extreme precipitation is crucial for engineering design and the action planning for protecting societies against such events. Extreme rainfall can produce heavy floods causing several damages to population centers and potential loss of lives. Multivariate extreme value statistics describes the behaviour of two or more variables at extreme levels. In this context, the multivariate vector under study is the 49-dimensional vector of weekly maxima of hourly rainfall recorded at French weather stations in the Fall season in the period 1993 - 2011. Thus, for each station, n = 228 values have been collected. Data are grouped in clusters as suggested by [1], where in each of the seven groups, seven