Robust models for mixed effects in linear mixed models applied to Small Area Estimation

Hierarchical models are popular in many applied statistics fields including Small Area Estimation. A well known model in this field is the Fay-Herriot model, in which unobservable parameters are assumed Gaussian. In Hierarchical models assumptions about unobservable quantities are difficult to check. Sinharay and Stern (2003) for a special case of the Fay-Herriot model, showed that violations of the assumptions about the random effects are difficult to assess using posterior predictive checks. They conclude that this may represent a form of model robustness . In this paper we consider two extensions of the Fay-Herriot model in which the random effects are supposed to be distributed according to either an Exponential Power (EP) distribution or a skewed EP distribution. The aim is to explore the robustness of the Fay-Herriot model for the estimation of individual area means as well as the Empirical Distribution Function of their ’ensemble’. Based on a simulation experiment our findings are largely consistent with those of Sinharay and Stern as far as the efficient estimation of individual small area parameters is concerned. On the contrary, when the aim is the estimation of the Empirical Distribution Function of the ’ensemble’ of small area parameters, results are more sensitive to the failure of distributional assumptions.