Original Article





In numerous practical applications, data from neighbouring small areas present spatial correlation. More recently, an extension of the Fay–Herriot model through the spatial (exponential) has been considered. This spatial area-level model like the fundamental area-level model (was first suggested by Fay III and Herriot ) has a powerful assumption of known sampling variance . Several methods have been suggested for smoothing of sampling variance and there is no unique method for sampling variance estimation, more studies need.


This research examines four techniques for sampling variance estimates including of Direct , Probability Distribution, Bayes and Bootstrap methods. We used households'  food expenditures (HFE) data 2013 and other socio-economic ancillary data to fit the read model and at last conduct a simulation study based on this data to compare the effects of four variance estimation methods on precision of small area estimates.


The best model on real data showed that the lowest and the highest HFE belonged to Pishva district (in Tehran province) with 26,707 thousand rials (TRs) and Omidiyeh (in Khouzestan province) with 101,961 TRs, respectively. Accordingly on simulation study, the probability distribution and direct methods, respectively and approximately had the smallest and the highest Root Average Mean Square Errors  (RAMSE)  for all conditions.


The results showed the best fitting with Direct method in real data and best precision with Probability Distribution method in simulation study.

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IssueVol 8 No 3 (2022) QRcode
SectionOriginal Article(s)
Spatiality small area estimation exponential structure household food expenditure sampling variance simulation

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