Bias Control for M-Quantile-Based Small Area Estimators

Projective outlier-robust M-quantile-based small area estimators can be substantially biased when the sample data contain representative outliers. In this paper we propose two new predictive type bias corrected versions of these estimators for continuous and discrete outcomes. Given both area level and individual level outliers in the population, these new estimators are more efficient than the robust-predictive and robust-projective estimators that have been proposed in the small area estimation literature. We also propose two estimators of the prediction mean-squared error of these estimators: one based on Taylor linearization and the other based on a new semi-parametric bootstrap method. We summarize the empirical evidence for these theoretical results in this paper, while in the Supplementary Material we describe in more detail how the properties of these M-quantile-based small area estimators have been assessed in model-based and design-based simulations, as well as in a realistic application focusing on estimation of average income and unemployment rates for local labor market areas in Italy.