Résumé
Rainfall amounts are measured daily at a network of rain gauge stations in a given area. We consider the annual maxima at each station in order to evaluate the impact of heavy rainfall. At a given station, these annual maxima are naturally modelled by the generalized extreme value (GEV) distribution. We assume that the GEV parameters vary smoothly over the area covering the rainfall stations. We propose a kernel based semi-parametric estimator to spatially interpolate theGEV parameters over the area. At an arbitrary location, the GEV parameters are obtained by maximizing the log-likelihood over the rainfall amounts observed in neighbouring locations weighted by the distance between locations. If there is a rain gauge at the location of interest, then this is very close in spirits to the model proposed by Wang et al [1]. However, we propose to use the estimator to predict the GEV parameters at ungauged sites and thus obtain a spatial estimation of the GEV parameters over the area. We investigate for 1D synthetic examples, the behaviour of the spatial kernel estimator. We develop a novel way to define neighbours based on similarity in distributions. Finally, we evaluate the proposed estimator on rainfall data from the Cevennes-Vivarais area, in the South of France.