Outlier Robust Small Area Estimation

Recently proposed outlier robust small area estimators can be substantially biased when outliers are drawn from a distribution that has a different mean from that of the rest of the survey data. This naturally leads one to consider an outlier robust bias correction for these estimators. In this paper we develop this idea, proposing two different analytical mean squared error estimators for the ensuing bias corrected outlier robust estimators. Simulations based on realistic outlier contaminated data show that the proposed bias correction often leads to more efficient estimators. Furthermore, the proposed mean squared error estimation methods appear to perform well with a variety of outlier robust small area estimators.