Dian Handayani, Khairil Anwar Notodiputro, Asep Saefuddin, I Wayan Mangku, Anang Kurnia
Small area estimation (SAE) addresses the estimation of parameters for population subsets when the sample itself is too small to produce reliable direct estimates. The standard method, empirical best linear unbiased prediction, uses a predictor under a linear mixed model that assumes normality of the variable of interest and independence among small areas. However, in practical studies, the distribution of the variable of interest tends to be positively skewed and there exists spatial dependence among the small areas. To address both of these, a previous study had proposed a spatial synthetic (SYNT) predictor that predicts non-sampled values of the variable of interest using its unconditional mean. The SYNT predictor is derived based on a unit-level spatial lognormal mixed model. Herein, we propose spatial empirical best predictor (SEBP) to improve the SYNT predictor by using its conditional mean to predict the non-sampled values of the variable of interest. We perform simulation studies to evaluate the performance of SEBP and compare them with those of the SYNT predictor and other existing methods. Our results reveal that the SEBP performs better in terms of the average relative bias and average relative root mean square error when the spatial correlation among small areas is small, medium or large. In an SAE application on the average monthly household per-capita expenditure for sub-districts in Bogor, Indonesia, the proposed SEBP provides better estimates than other established methods. © 2025
Statistics Study Program, Universitas Negeri Jakarta, Jakarta, 13220, Indonesia; School of Data Science, Mathematics, and Informatics, IPB University, Jawa Barat, 16680, Indonesia
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