An Alternative Bayesian Estimator of Small Proportion Using Binomial Group Testing
Group testing has been used for estimating proportion in certain areas. Bayes Estimator and type-II Maximum Likelihood Empirical Bayes (MLEB) Estimator have been studied in the literature. In this article, we first discuss some properties of the Bayes Estimator. Then we show the existence and uniqueness of the MLE of a hyper-parameter appearing in the prior of the proportion. Finally, we propose an Alternative Empirical Bayes (AEB) Estimator. Based on our heavy simulation work, it appears that as bias is concerned, the performance of the AEB and the Burrows estimator are about the same and both are better than the MLEB; on the other hand, the AEB has smaller MSE than both Burrows estimator and the MLEB estimator.