Some Empirical Bayes Estimations Of Success Probability Of Boinomial And It's Optimum

The thought of Empirical Bayes method was first come from von Mises(1942), and then it was formally put forward by Robbins in 1955,to tempt to resolve the difficulties when Bayes method was used, but prior was unkown, so it was in the field of statistics. A basic problem of Empirical Bayes estimate in theoretical research is to look for suitable Empirical Bayes estimation and to prove it to be asymptotic optimal. On this problem a mighty advance is now made in exponential and truncated family of distributions, but the proof is verbose.In this thesis, the Empirical Bayes estimations and multiple Empirical Bayes estimations of success probability theta of Boinomial distribution were given out by moment estimate when theta followed different priors, and the superiority of these estimations was simply discussed. With analog computation some of these estimates was found to be superior to the linear Empirical Bayes estimate given out by Robbins and these estimats were proved to be strong consistent and asymptotic optimal(a.o.). So the results were satisfactory.