Small area estimation is becoming important in survey sampling due to a growing demand for reliable small area statistics from both public and private sectors. It is now widely recognized that direct survey estimates for small areas are likely to yield unacceptably large standard errors due to the smallness of sample sizes in the areas. This makes it necessary to "borrow strength" from related areas to find more accurate estimates for a given area or, simultaneously, for several areas. This has led to the development of alternative methods such as synthetic, sample size dependent, empirical best linear unbiased prediction, empirical Bayes and hierarchical Bayes estimation. The present article is largely an appraisal of some of these methods. The performance of these methods is also evaluated using some synthetic data resembling a business population. Empirical best linear unbiased prediction as well as empirical and hierarchical Bayes, for most purposes, seem to have a distinct advantage over other methods.
"Small Area Estimation: An Appraisal." Statist. Sci. 9 (1) 55 - 76, February, 1994. https://doi.org/10.1214/ss/1177010647