A quasi-Bayesian Approach to Small Area Estimation Using Spatial Models

Abstract

The empirical best linear unbiased prediction (EBLUP) method has been the dominant model-based approach in small area estimation. As an alternative to this frequentist method, the observed best prediction (OBP) method, also frequentist, was proposed by Jiang et al.[ 11 ] where the parameters of the model are estimated by minimizing an objective function which is implied by the total mean squared prediction error. In a recent article, Datta et al.[ 6 ] followed a general Bayesian approach, proposed recently by Bissiri et al.[ 2 ], to develop a quasi-Bayesian method by appropriately calibrating the objective function for the OBP method for the Fay-Herriot model. In a different article, Chung and Datta[ 4 ] demonstrated that in the absence of covariates with good predictive power the small area estimates from the standard Fay-Herriot model can be improved by using spatially dependent random effects. In this article, we develop a quasi-Bayesian small area estimation method using several spatial alternatives to the independent Fay-Herriot random effects model. Evaluation of the proposed method based on an application to estimation of four-person family median incomes for the U.S. states shows its usefulness. Limited but related simulation studies for the median incomes application reinforce our conclusion. AMS Subject Classification: 62F 15, 62D99