PhD Thesis with advisors Eustasio del Barrio and Fabrice Gamboa, defended on the 16th of July, 2007, before the tribunal composed by Profesors Jean-Marc Azaïs, Bernard Bercu, Eustasio del Barrio, Fabrice Gamboa and Carlos Matrán.
This thesis is composed of three main parts. In the first part, we study some asymptotic properties of multiple integrals with respect to the empirical process. The second part is devoted to the study of the asymptotic efficiency of the Wasserstein test. The equivalence of the Wasserstein statistic with a double integral with respect to the empirical process allows us to apply the results of the first part. A simulation study is added to the study of the asymptotic power. The third part deals with large deviations for L-statistics. A large deviations principle is obtained using the topology of the Wasserstein distance on the space of measures, under conditions on the extremes.