Robust linear mixed models for Small Area Estimation

Hierarchical models are popular in many applied statistics fields including Small Area Estimation. One well known model employed in this particular field is the Fay-Herriot model, in which unobservable parameters are assumed to be Gaussian. In Hierarchical models assumptions about unobservable quantities are dicult to check. In this present paper we consider two extensions of the Fay-Herriot model in which the random effects are assumed to be distributed according to either an Exponential Power (EP) distribution or a skewed EP distribution. We aim 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'. Our findings, which are based on a simulation experiment, are largely consistent with those of Sinharay and Stern (2003) as far as the efficient estimation of individual small area parameters is concerned. However, when estimating the empirical distribution function of the 'ensemble' of small area parameters, results are more sensitive to the failure of distributional assumptions.