Bayesian Semiparametric Hierarchical Empirical Likelihood Spatial Models

Abstract

We introduce a general Bayesian hierarchical framework that incorporates a flexible nonparametric data model specification through the use of empirical likelihood methodology, which we term semiparametric hierarchical empirical likelihood (SHEL) models. Although general dependence structures can be readily accommodated, we focus on spatial modeling, a relatively underdeveloped area in the empirical likelihood literature. Importantly, the models we develop naturally accommodate spatial association on irregular lattices and irregularly spaced point referenced data. We illustrate the methodology using a spatial SHEL Fay-Herriot model and apply it demographic data from the American Community Survey. We demonstrate the superior performance of our model, in terms of mean squared prediction error, over standard parametric analyses.