Bayesian Point Estimation and Predictive Density Estimation for the Binomial Distribution with a Restricted Probability Parameter
Statistics Theory
2021-09-13 v2 Methodology
Statistics Theory
Abstract
In this paper, we consider Bayesian point estimation and predictive density estimation in the binomial case. After presenting preliminary results on these problems, 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 less than or equal to a known constant. The case where there are both a lower bound restriction and an upper bound restriction is also treated. Then our problems are shown to be related to similar problems in the Poisson case. Finally, numerical studies are presented.
Cite
@article{arxiv.2103.00518,
title = {Bayesian Point Estimation and Predictive Density Estimation for the Binomial Distribution with a Restricted Probability Parameter},
author = {Yasuyuki Hamura},
journal= {arXiv preprint arXiv:2103.00518},
year = {2021}
}
Comments
29 pages, 4 figures; Theorem 3.3 and Sections 4 and 6 have been added