A Bayesian Semiparametric Fay-Herriot-type model for Small Area Estimation

Borrowing strength in small area estimation is most often achieved through mixed effects regression models. The default normality assumption for random effects is difficult to check, as they are latent variables. Missing covariates can lead to multimodal distributions of random effects; the distribution may also be skewed. Clearly the difficulties in model checking arise for any other parametric assumption. Estimation of the random effects is crucial for predicting small area quantities, and the effect on model estimates of parametric assumptions is shown to be important. In this paper a semiparametric Bayesian linear mixed effects model is analysed, in which the random effects are modelled through a Dirichlet process. The application focuses on a Fay-Herriot-type area level model; in this context, the main aim is to assess improvements in precision of small area predictions.