Results of a Simulation Study to Measure the Effectiveness of Empirical Bayes' Estimates of Multiple Probabilities

摘要

Empirical Bayes' methods have been used by Brier, Zacks, and Marlow (1985) to estimate a set of parameters where each parameter is a k-dimensional vector consisting of the probabilities that a Marine combat unit will successfully complete requirements in each of k different categories. This paper assesses the performance of the empirical Bayes' estimators by simulating parameters from a multivariate normal distribution and simulating the observed sample counts from the binomial distribution. The empirical Bayes' estimators are compared to the sample proportion in terms of mean square error and absolute deviations. Using both criteria, the Bayes' estimators are shown to provide considerable improvement across a wide range of parameter values. The results suggest that empirical Bayes' estimates are useful in a variety of situations where a set of multivariate binomial probabilities are to be estimates.