Admissible and minimax estimation of the parameter n in the binomial distribution

In this paper, the problem of estimating the parameter n of the binomial distribution is considered under the assumption of both infinite and finite parameter spaces. A class of estimators, which include as a special case Sadooghi-Alvandiʹs [Ann. Statist. 14 (1986) 1634] estimator is considered; and the necessary and sufficient conditions for this class of estimators to be admissible are obtained, along with a new proof on the admissibility of Sadooghi-Alvandiʹs estimator. Furthermore, the minimax property of some estimators is investigated.