Extreme value theory and applications in environment
In the first two chapters, we try to answer two questions that are critical in climatology. The first one is to know whether a change in the behaviour of the temperature extremes occured between the beginning of the century and today. We suggest to use a version of the Kullback Leibler divergence tailored for the extreme value context. We provide some theoretical and simulation results to justify our approach. The second question is to decide where to remove stations from a network to lose the least information about the behaviour of the extremes. An algorithm called the Query By Committee is developed and applied to real data. The last chapter of the thesis deals with a more theoretical subject which is the robust estimation of a Weibull type tail index in presence of random covariates. We propose a robust estimator based on a criterion ofminimization of the divergence between two densities and study its properties.