Bayesian Point Estimation and Predictive Density Estimation for the Binomial Distribution with a Restricted Probability Parameter

In this paper, we consider Bayesian point estimation and predictive density estimation in the binomial case. First, preliminary results on these problems are presented. Next, we compare the risk functions of the Bayes estimators based on the truncated and untruncated beta priors and obtain dominance conditions when the probability parameter is smaller than a known constant. Finally, our problem is shown to be related to a similar problem in the Poisson case.