Global-Local Priors for Spatial Small Area Estimation

Abstract

Small area estimation is gaining increasing popularity among survey statisticians. Since the direct estimates of small areas usually have large standard errors, model-based approaches are often adopted to borrow strength across areas. The models often use covariates to link different areas and random effects to account for the additional variation. In the classic Fay-Herriot model, the random effects are assumed to have independent normal distributions with a shared variance. Recent studies showed that random effects are not necessary for all areas, so global-local priors have been introduced in Tang et al.[26] to effectively characterize the sparsity in random effects. This article introduces global-local priors in the context of small area estimation where the area level random effects exhibit a spatial structure. This generalizes the findings of Tang et al.[26] where independence of the area level effects is assumed. Our findings are illustrated via both simulation and real data examples. AMS subject classification: 62D05, 62M30.