A review of small area estimation problems and methodological developments

Small area estimation has received much attention in recent decades due to increasing demand for reliable small area estimates from both public and private sectors. Traditional direct estimation requires the domain-specific sufficiently large sample. In reality domain specific sample data are not large enough for all small areas (even zero for some small areas) to provide adequate statistical precision of their estimates. This makes it necessary to 'borrow strength' from data on related multiple characteristics and/or auxiliary variables from other neighbouring areas through appropriate models, leading to indirect or model based estimates. Most of the review articles in small area estimation have highlighted methodologies which are fully based on various statistical models and theories. For example, implicit models approaches consist of synthetic, composite and demographic estimations. As well, explicit area level and unit level model based approaches have been widely studied through various statistical tools and techniques including (empirical-) best linear unbiased prediction (E-BLUP), empirical Bayes (EB) and hierarchical Bayes (HB) methods. Another type of technique called 'spatial microsimulation' has also provided small area estimates during the last decade. These models are based on economic theory and using quite different methodologies. This paper reviews the overall methodologies for obtaining small area estimates which have emerged over the last few decades with particular emphasis given to the indirect estimations. I classified the methodologies that have been developed for indirect small area estimation as 1) the statistical model-based approaches and 2) the geographical microsimulation approaches. A thorough overview on various microsimulation models shows that spatial microsimulations are robust and have advantages over others. In contrast to statistical approaches, the spatial microsimulation model based geographic approaches can operate through different reweighting techniques such as GREGWT and combinatorial optimisation (CO). A comparison between reweighting techniques reveals that they are using quite different algorithms and that their properties also vary. However their performances are fairly similar according to the advantages of spatial microsimulation modelling.