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SMALL AREA ESTIMATION METHOD WITH EMPIRICAL BAYES BASED ON BETA BINOMIAL MODEL IN GENERATED DATA

*Ferra Yanuar  -  Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Andalas, Indonesia
Rahmatika Fajriyah  -  Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Andalas, Indonesia
Dodi Devianto  -  Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Andalas, Indonesia
Open Access Copyright (c) 2021 MEDIA STATISTIKA under http://creativecommons.org/licenses/by-nc-sa/4.0.

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Abstract
Small Area Estimation is one of the methods that can be used to estimate parameters in an area that has a small population. This study aims to estimate the value of the binary data parameter using the direct estimation method and an indirect estimation method by using the Empirical Bayes approach. To illustrate the method, we consider three conditions: direct estimator, empirical Bayes (EB) with auxiliary variables, and empirical Bayes without auxiliary variables. The smaller value of Mean Square Error is used to determine the better method. The results showed that the indirect estimation methods (EB method) gave the parameter value that was not much different from the direct estimation value. Then, the MSE values of indirect estimation with an auxiliary variable are smaller than the direct estimation method.
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Keywords: SAE; Empirical Bayes Method; Beta-Binomial Model.

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