A necessary and sufficient condition for generalized admissibility of Bayes estimate
(Central South University, Changsha 410083, China)
Abstract: A definition of generalized admissibility of Bayes estimates has been given. This generalized admissibility is a rule to identify whether Bayes estimates is acceptable or not under the condition of incorrect prior information. In this paper, a sufficient and necessary condition for the generalized admissibility is derived under quadratic loss. From this we can conclude that, when deviation of prior mean and deviation of prior variance do not go beyond the bound, the Bayes estimation is acceptable and it is discussed that how the deviation of the prior information influences on generalized admissibility. Because the precise distribution of prior information is unknown, the example gives a way to select the prior distribution. The example shows that this method is efficient and feasible.
Key words: Bayes estimate； generalized admissibility； inaccurate prior； quadratic loss； Bayes risk