Small area estimation of general parameters: Bayesian transformed spatial prediction approach

Abstract

For estimating area-specific parameters such as poverty indicators in a finite population, estimators based only on the area-specific samples have typically high variability due to small sample sizes, and model-based methods are recognized to be useful to increase the accuracy of the estimation by borrowing information from related areas. This article proposes an Bayesian approach to this problem based on random effects models. To address the non-normality of response variables and possible spatial correlations among geographically neighboring areas, we introduce random effects models with a parametric family of transformations and spatially correlated random area effects. We assign prior distributions on unknown parameters including transformation and spatial correlation parameters and provide an efficient posterior computation algorithm for estimation and inference for area-specific population parameters via Markov Chain Monte Carlo. We demonstrate the performance of the proposed methods together with existing methods through simulation and empirical studies.