On comparison some estimators in small area study

Efron and Morris (1975) gave an amusing example of batting averages of major league baseball players in the United States, to illustrate the superiority of James Stein estimators over direct estimators. In this paper, we include eight more competitors and attempts to seek a best estimator of all. These new estimators include the overall sample proportion, a synthetic estimator using the previous year batting average, two composite estimators that we mentioned, the Bayes estimators using either noninformative or informative prior distribution. We use about 370 more times at batting average was taken as the true value. Since the true values are assumed to be known, we can compute the relative overall accuracies. Four more criteria have been included to increase the selection results.