Pseudo-Bayesian Small-Area Estimation

In sample surveys, a subpopulation is referred to as a “small area” or “small domain” if it does not have a large enough sample that alone will yield an adequately accurate estimate of a characteristic. In small-area estimation, the sample size from various subpopulations is often too small to accurately estimate its mean, and so one borrows strength from similar subpopulations through an appropriate model based on relevant covariates. The empirical best linear unbiased prediction (EBLUP) method has been the dominant frequentist model-based approach in small-area estimation. This method relies on estimation of model parameters based on the marginal distribution of the data. As an alternative to this method, the observed best prediction (OBP) method estimates the parameters by minimizing an objective function that is implied by the total mean squared prediction error. We use this objective function in the Fay–Herriot model to construct a pseudo-posterior distribution for the model parameters under nearly noninformative priors for them. Data analysis and simulation show that the pseudo-Bayesian estimators (PBEs) compete favorably with the OBPs and EBLUPs. The PBE estimates are robust to mean misspecification and have good frequentist properties. Being Bayesian by construction, they automatically avoid negative estimates of standard errors, enjoy a dual justification, and provide an attractive alternative to practitioners.