Study of the asymptotic properties of bayes estimators.

Summary The main part of this thesis concerns the asymptotic predictions of some confidence regions. It is organized around three axes: the first one concerns the study of Bayesian and frequentist covers of two types of confidence regions, the hpd regions and the joint bilateral intervals, when the observations are not discrete. In these two cases, asymptotic developments of the a posteriori and frequentist covers are obtained, as well as conditions of agreement between the two approaches. The second axis concerns the existence of asymptotic developments, at higher orders, of frequentist covers of some confidence regions in the discrete case. The third axis studies the effectiveness of continuity corrections on these asymptotic developments (still in the discrete case), determines asymptotic properties at higher orders of these rcorrected regions. For each of these three axes, the existence of nuisance parameters is considered. The last chapter deals with point estimation by studying the asymptotic bayes risk for a large family of loss functions.