Semiparametric Bayesian Small Area Estimation Based on Dirichlet Process Priors

Small area estimation concerns the problem of releasing estimates for domains that are not planned by design in statistical surveys. For such domains the observed sample size may often be too small to allow for accurate estimation of aggregates of interest. To borrow strength from related domains, the vast majority of small area models relies on mixed effects regression models. Whereas inference on the fixed effects is shown to be robust to deviations from normality, estimation of the random effects is crucial for predicting small area quantities. The potential impact of distributional assumptions on the random effects is shown to be important; missing covariates can lead to multimodal distributions for the random effects; the latter may also be skewed. Any parametric assumption, applying to nonobservable quantities, is difficult to check. This contribution examines a Bayesian semiparametric version of the Fay-Herriot model in which the default normality assumption for the random effects is replaced by a nonparametric specification, based on the Dirichlet process. Viability of the approach and the effect of introducing a flexible specification of the random effects are investigated through an application to simulated data.