Forecasting the batting averages of korean pro baseball players using stein's estimator

Abstract

In 1961, James and Stein proposed some estimator of the mean of a multivariate normal distribution which improved the squared error risk function compared with usual maximum likelihood estimator (MLE). Stein``s estimator and some emperical Bayes estimator which has the same property can be applied to predict the batting averages of the baseball players. The empirical Bayes resorted to Efron and Morris (1973) who extended the Stein estimator to general empirical Bayes estimator. This paper is tried to predict the seasonal batting averages of players in Korean Pro Baseball League in the way of Efron``s method and to improve it on the point of experience.