Improved Empirical Bayes Estimation in Group Testing Procedure for Small Proportions

Group testing has been long recognized as an efficient method to classify all the experimental units into two mutually exclusive categories: defective or not defective. In recent years, more attention has been brought to the estimation of the population prevalence rate p of a disease, or of some property, using group testing. In this article, we propose two scaled squared-error loss functions, which improve the Bayesian approach to estimating p in terms of minimizing the mean squared error (MSE) of the Bayes estimators of p for small p. We show that the new estimators are preferred over the estimator from the usual squared-error loss function and the maximum likelihood estimator (MLE) for small p.