?-Admissible Estimators for Normal and Poisson Means

The criterion of admissibility has been considered as one of the most important criterion in decision theory and many important results have been contributed in this direction. In this article, we propose a more flexible criterion, so-called ?-admissibility (which can be considered as weak admissibility), which generates a monotone sequence of classes of estimators. The limit of this sequence, class of 0⁺-admissible estimators, is the smallest class including the class of usual admissible estimators, which also belongs to the monotone sequence. Some sufficient and necessary conditions are proposed for ?-admissibility and 0⁺-admissibility. Under some weighted square loss, it can be shown that the usual MLE is 0⁺-admissible for the multivariate normal distribution and the multivariate Poisson distribution.