Robust Estimation of Small Area Means and Quantiles

Small area estimation techniques have typically relied on plug-in estimation based on models containing random area effects. More recently, regression M-quantiles have been suggested for this purpose, thus avoiding conventional Gaussian assumptions, as well as problems associated with the specification of random effects. However, the plug-in M-quantile estimator for the small area mean can be shown to be the expected value of this mean with respect to a generally biased estimator of the small area cumulative distribution function of the characteristic of interest. To correct this problem, we propose a general framework for robust small area estimation, based on representing a small area estimator as a functional of a predictor of this small area cumulative distribution function. Key advantages of this framework are that it naturally leads to integrated estimation of small area means and quantiles and is not restricted to M-quantile models. We also discuss mean squared error estimation for the resulting estimators, and demonstrate the advantages of our approach through model-based and design-based simulations, with the latter using economic data collected in an Australian farm survey.