A Comparison Small Area Estimation for Skewed Data with EBLUP and Hierarchical Bayes Approaching using Rao-Yu Model

Abstract

Small Area Estimation (SAE) is a method based on modeling for estimating small area parameters, that applies the Linear Mixed Model (LMM) as its basic. It is conventionally solved with Empirical Best Linear Unbiased Prediction (EBLUP). The main requirement for LMM to produce high precision estimates is normally distributed for its sampling error. However, the researching data namely per capita food expenditure for food crop farmers’ households in Southeast Sulawesi Province has been positively skewed. Applying EBLUP for positively skewed data will produce less accurate estimates. Meanwhile, doing a transformation process will potentially produce biased estimates. The Hierarchical Bayes (HB) approaching often known as Full Bayesian is more flexible regarding normality assumptions and can determine distribution based on data. Because this research will carry out estimates at the district/city level throughout Southeast Sulawesi Province, totaling 17 regions, the efficiency of the estimates can be increased by using the SAE Rao-Yu model which includes area and time random effects. For this reason, this study compares SAE modeling with the EBLUP and HB approaches which are assumed to follow normal, log-normal, and skew-normal distributions. By comparing the Relative Root Mean Square Error (RRMSE), Deviance Information Criterion (DIC), and Coefficient of Variation (CV) values, it is concluded that estimates from the log-normal and skew-normal SAE HB models are more efficient than the SAE EBLUP and normal HB models. However, the SAE estimate that is closer to the direct estimation results is the skew-normal SAE HB.