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Abstract:
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National statistical agencies are regularly required to produce estimates about various subpopulations, formed by demographic and/or geographic classifications, based on a limited number of samples. Traditional direct estimates computed using only samples from individual subpopulations are usually unreliable due to small sample sizes. Subpopulations with insufficient samples are termed small areas. To improve on less reliable direct area estimates, model-based estimates, which borrow information from suitable auxiliary variables, have been extensively proposed in the literature. In a pioneering article, Ghosh and Meeden (JASA, 1986) presented an empirical Bayes approach to producing reliable estimates of small area means by borrowing strength from other small areas. In this talk, we will review many subsequent fully Bayesian generalizations of this important idea that also utilize other auxiliary information. We will present noninformative hierarchical Bayesian robust estimates of small area means for unit level data which may contain outliers. Our simulations show that the proposed Bayesian point and interval estimates of small area means enjoy good frequentist properties.
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