Ungünstige Verteilungen bei einparametrigen Parameterschätzproblemen

Summary One of the commonly used methods for determining minimax point estimators is based on least favorable distributions, because Bayes estimators with respect to a least favorable distribution are frequently minimax point estimators. Therefore it is worthwhile to investigate the structure of least favorable distributions. In the present paper it will be proved that, under certain conditions, each least favorable distribution is finite discrete. We give sufficient conditions for point estimation problems with the property that each least favorable distribution is finite discrete. Some examples are presented.