This research project focuses on Bayesian and likelihood based multilevel models for small area estimation. These methods will be compared and contrasted against some of the existing methods, such as the pseudo maximum likelihood, penalized quasilikelihood, etc. Some of the novel features of this research will be the use of stratum varying regression coefficients, new priors for the variance-covariance matrix rather than the standard Wishart prior, development of small area estimation models allowing measurement errors for covariates, use of hierarchical likelihood in the context of small area estimation, and the use of survey weights for small area estimation. One of the major applications of this project will be the estimation of income and poverty for states and counties, and possibly even for lower levels of geography such as census tracts and school districts (when data become available) between decennnial censuses. However, the methods are fairly general, and can be applied to other studies as well. Among others, these methods will be applied to study youth unemployment for small areas based on the Scottish School Leavears Survey, effectiveness of schools and student character in an education survey conducted by the Inner London Education Authority, and a British Social Attitudes Survey.
The terms "small area'' or "local area" are commonly used to denote a small geographical area, such as a county, a municipality, or a census division. They may also describe a "small domain;" that is, a small subpopulation such as a specific age-sex-race group of people within a large geographical area. In these days, there is a global need for reliable small area statistics both from the private and public sectors. There are increasing government concerns with issues of distribution, equity, and disparity. For example, there may exist geographical subgroups within a given population that are handicapped in many respects, and need definite upgrading. Before taking remedial action, there is a need to identify such regions, and accordingly, one must have statistical data at the relevant geographical levels. Small area statistics also are needed in the apportionment of government funds, and in regional and city planning. In addition, there are demands from the private sector since the policy-making of many businesses and industries relies on local socio-economic conditions. Thus, small area estimation techniques have global applicability, and are useful for diverse applications.
