Bootstrap Method in Estimation of Mean Squared Error of Beta-Bernoulli Model

Small area estimation is defined as a statistical technique to estimate small sub population of a certain area. There are several method of small area including Empirical Bayes (EB), Hierarchical Bayes (HB) and Empirical Best Linear Unbiassed Prediction (EBLUP). EB method is one of methods in small area estimation for count or binary data. Estimation with EB method is based on posterior which its parameter is estimated by data. One application of EB method for binary data is Beta-Bernoulli Model. In this study, Mean Squared Error (MSE) of the EB estimator was evaluated by Bootstrap method by theory and empirical though simulation by using Ri386 3.4.3 software. The results of this study showed that EB estimator is biased, and the Bootstrap MSE becomes smaller when the amount of areas get greater.