RESUMEPour des familles exponentielles de lois, nous estimons des paramttres d'int6rEt qui ne sont pas les paramttres naturels. Nous ttablissons que, sous une condition de cornpacite, les estimateurs admissibles de ces paramttres sont limites d'estimateurs de Bayes et s'expriment sous une forme fonctionnelle particulibre. Un cas particulier important du cadre CtudiC porte sur I'estimation de la moyenne d'une loi normale multidimensionnelle dont la variance n'est connue qu'8 un facteur multiplicatif prbs. Nous diduisons du rtsultat general une condition nkcessaire d'admissibilite pour les estimateurs B rktrkisseur. ABSTRACTConsidering exponential families of distributions, we estimate parameters which are not the natural parameters. We prove that the admissible estimators of these parameters are limits of Bayes estimators and can be expressed through a given functional form. An important particular case of this model pertains to the estimation of the mean of a multidimensional normal distribution when the variance is known up to a multiplicative factor. We deduce from the main result a necessry condition for the admissibility of matricial shrinkage estimators.

Necessary admissibility conditions allow for the reduction of the classes of estimators to consider when there is no complete class result or when it is too difficult to check Stein's sufficient admissibility conditions. STUB conditions were introduced by Brown [6] and developed by Hwang [18], taking advantage of the Stein phenomenon with some truncated shrinkage estimators. In this paper, we present some STUB conditions in the particular case of a continuous exponential family with a nuisance parameter δ and show the implications of these conditions in normal and gamma examples.