New Bias Calibration for Robust Estimation in Small Areas

Abstract: Using sample surveys as a cost effective tool to provide estimates for characteristics of interest at population and sub-populations (area/domain) level has a long tradition in "small area estimation". However, the existence of outliers in the sample data can significantly affect the estimation for areas in which they occur, especially where the domain-sample size is small. Based on existing robust estimators for small area estimation we propose two novel approaches for bias calibration. A series of simulations shows that our methods lead to more efficient estimators in comparison with other existing bias-calibration methods. As a real data example we apply our estimators to obtain \textit{Gini} coefficients in labour market areas of the Tuscany region of Italy, where our sources of information are the EU-SILC survey and the Italian census. This analysis shows that the new methods reveal a different picture than existing methods. We extend our ideas to predictions for non-sampled areas.