In this paper,a linear empirical Bayes estimator of unknown parameter vector is constructed in linear regression model. Under some conditions, its asymptotic optimal convergence is proveded with convergent rate O (). Song's results are improved esentially.
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.)