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BETA-BINOMIAL MODEL IN SMALL AREA ESTIMATION USING HIERARCHICAL LIKELIHOOD APPROACH

*Etis Sunandi scopus  -  Department of Statistics, IPB University, Indonesia, Indonesia
Khairil Anwar Notodiputro  -  Department of Statistics, IPB University, Indonesia, Indonesia
Indahwati Indahwati  -  Department of Statistics, IPB University, Indonesia, Indonesia
Agus Mohamad Soleh  -  Department of Statistics, IPB University, Indonesia, Indonesia
Open Access Copyright (c) 2023 MEDIA STATISTIKA under http://creativecommons.org/licenses/by-nc-sa/4.0.

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Abstract
Small Area Estimation is a statistical method used to estimate parameters in sub-populations with small or even no sample sizes. This research aims to evaluate the Beta-Binomial model's performance for estimating small areas at the area level. The estimation method used is Hierarchical Likelihood (HL). The data used are simulation data and empirical data. Simulation studies were used to investigate the proposed model. The estimator's Mean Squared Error of Prediction (MSEP) and Absolute Bias (AB) estimator values determine the best estimation criteria. An empirical study using data on the illiteracy rate at the sub-district level in Bengkulu Province. The results of the simulation study show that, in general, the parameter estimators are nearly unbiased. Proportion prediction has the same tendency as parameters. Finally, the HL estimator has a small MSEP estimator. The results of an empirical study show that the average illiteracy rate in Bengkulu province is quite diverse. Kepahiang District has the highest average illiteracy rate in Bengkulu Province in 2021.
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Keywords: Area level; Binary Response; Illiteracy rate; MSEP; Simulation; Small sample

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