How to aggregate density estimates?  ALEXANDRE TSYBAKOV Université Paris 6                                                                           Assume that we have a given collection of density estimates of general nature. Can we find a aggregated density estimate that behaves itself approximately at least as good as the best one in this collection, or as the best one in its convex hull, or as the best one in its linear envelope? Here the word "approximately" means that aggregation, in general, introduces some error, in other words there is a price to pay for aggregation. The purpose of this talk is to show that aggregated estimators that achieve the three goals mentioned above can be constructed by a general procedure which is optimal since in a sense it pays the minimal possible price for aggregation. This approach gives an improvement of various previously known results about the choice of smoothing parameter and model selection, and allows to explore more complex models than the traditional ones.