# SMALL AREA ESTIMATION WITH HIERARCHICAL BAYES FOR CROSS-SECTIONAL AND TIME SERIES SKEWED DATA

• Titin Yuniarty Department of Statistics, Faculty of Mathematics and Natural Sciences, IPB University, Indonesia
• Indahwati Indahwati Department of Statistics, Faculty of Mathematics and Natural Sciences, IPB University, Indonesia
• Aji Hamim Wigena Department of Statistics, Faculty of Mathematics and Natural Sciences, IPB University, Indonesia
Keywords: Hierarchical Bayes, Cross-Sectional and Time Series, SAE, Skew-normal

### Abstract

Small Area Estimation (SAE) is a method based on modeling for estimating small area parameters, that applies 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. The observation unit is food crop farmer households from Sulawesi Tenggara Province to estimate food and non-food per capita expenditure at the district/city level using SAE that has been positively skewed. Applying EBLUP for positively skewed data will result less accurate estimates. Meanwhile, transformation will be potentially result biased estimates. Therefore, the problem of skewed data and small area level in this research was completed by Hierarchical Bayes (HB) on combination cross-sectional and time series under skew-normal distribution assumption. The results obtained were skew-normal SAE HB model was significantly reducing Relative Root Mean Squared Error (RRMSE) than the direct estimation. It indicates that SAE modeling is able to provide a shrinkage effect on the direct estimation results. But, there is slightly different interpretating between direct estimation and skew-normal SAE HB. It is possible because the modeling used assumption that the autocorrelation coefficient is equal to 1 or known as the random walk effect. However, in reality, Susenas is not a panel data, so unit of observation for each time period may be different. Therefore, further research should be compared it with the skew-normal or another skewed distribution that assumes the autocorrelation coefficient is unknown and should be estimated in the model.

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Published
2024-03-01
How to Cite
[1]
T. Yuniarty, I. Indahwati, and A. Wigena, “SMALL AREA ESTIMATION WITH HIERARCHICAL BAYES FOR CROSS-SECTIONAL AND TIME SERIES SKEWED DATA”, BAREKENG: J. Math. & App., vol. 18, no. 1, pp. 0493-0506, Mar. 2024.
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Articles