Journal of Official Statistics, Vol.5, No.2, 1989. pp. 143–156
A Bayesian Approach to Small Domain Estimation
Kung-Jong Lui and William G. Cumberland
Abstract:Samples designed to provide an estimate of a feature of the entire population are often used secondarily to produce estimates of characteristics of subpopulations. Procedures depending on the distribution created by the sampling plan are usually not applicable due to the small subdomain sample sizes. Synthetic estimators and ratio-correlation estimators are difficult to evaluate with respect to the sampling plan and hence cannot provide a measure of error. In this paper, Bayesian estimators which are generalizations of the least-squares estimators of Holt, Smith, and Tomberlin (1979) are proposed. The estimators can easily incorporate auxiliary information from previous surveys with data from the current sample. A brief discussion of the robustness of the proposed Bayesian estimators is given. Simultaneous confidence intervals for all subdomains are also derived. The results are illustrated with an example using 26 health districts in Los Angeles County.
Keywords:Least-squares; Bayesian; super-population.
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