Benchmarking hierarchical Bayesian small area estimators in the percentage of poverty at sub-districts level in Central Java

Abstract

Solving poverty is the biggest global challenge, so it becomes the first goal in the Sustainable Development Goals (SDGs). The availability of accurate data is an important aspect to support poverty reduction strategies. Statistics Indonesia (BPS) has not been able to calculate the percentage of poverty up to small areas, such as sub-districts, because samples in the survey were not representative. Small Area Estimation (SAE) is a method used to estimate a small area with less or no sample. The problem arises when the estimator produced is not the same as the official statistics published for the higher level. The SAE often involves constructing predictions with an estimated model followed by a benchmarking step. In the benchmarking operation, the predictions are modified so that weighted sums satisfy constraints. In this study, Hierarchical Bayesian (HB) area level models are used to estimate the sampled and non-sampled areas. Posterior means and posterior variances of parameters of interest are first obtained using the Markov Chain Monte Carlo (MCMC) method. Then the HB estimators (posterior means) are benchmarked to obtain Benchmarked HB (BHB) estimators. Posterior Mean Squared Error (PMSE) is then used to measure uncertainty for the BHB estimators. The PMSE can be represented as the sum of the posterior variance and the squared difference of HB and BHB estimators. The evaluation of the HB and BHB estimators was carried out in the context of the estimated percentage of poverty at sub-district level in Central Java, Indonesia.