On the admissibility for the MLE in certain one parameter discrete distribution model

For estimation problems, an interesting question is whether the maximum likelihood estimator(MLE) is admissible or not under squared error loss. It is somewhat surprising that in many situations the admissibility of the MLE is still an open question. The aim of this research is to study the admissibility of the MLE for certain one parameter discrete probability models, that is described as P(x|θ) = c(x, θ)(1.θ)a(x)θb(x), where 0. θ. 1. For proving admissibility, we will use the stepwise Bayes method. This method is introduced in Hsuan and developed by Meeden and Ghosh(1981), Brown(1981) , Funo(1994). See also Ghosh and Meeden(1997). In section 1, we will briefly describe the stepwise Bayes method. Applying this method, the admissibility of θMLE under squared error loss when c(x, θ) = c(x) and some more mild conditions are satisfied was presented by Funo(1994). In section 2, the main theorem, which is an extension of this result, will be given. Several examples which can be shown of their admissibility by using the main theorem(Theorem 3) will be given in section 3. Further extension will be discussed in section 4