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Abstract
In a sample survey, a subpopulation is referred to as a "small area" if its sample is not large enough to yield direct estimates of adequate precision. One main interest in small area estimation is estimation of small area means. The observed best prediction (OBP) is a model-based prediction procedure for small area means that has been shown to be more robust than the empirical best linear unbiased prediction (EBLUP) against model misspecifications. We derive a pseudo-Bayesian alternative to the OBP under the Fay-Herriot model by converting the OBP objective function to a likelihood function. Real data examples and simulation studies show that the pseudo-Bayesian estimator (PBE) competes favorably with the OBP. In terms of interval estimation, the PBE credible interval attains the nominal coverage probability, while the OBP confidence interval exhibits unsatisfactory coverage. In addition to the PBE, we propose two compromise pseudo-Bayesian estimators (CPBE) of small area means using regression weights that compromise between those of the EBLUP and OBP. Real data examples show that the CPBEs can outperform the EBLUP, OBP, and PBE in terms of both accuracy and stability of the estimates. Lastly, we consider a problem where direct estimates are available only at a higher level of aggregation instead of the desired lower level of small areas. We generalize the Fay-Herriot model and propose a hierarchical Bayesian version of the model to estimate the lower level small area means. We decompose the posterior variance of small area mean and identify the source of increase in uncertainty caused by using aggregate information. A real data example is provided, where direct estimates at different levels of small areas are considered.