Robust Small Area Estimation Under Unit Level Models

Small area estimation has received considerable attention in recent years because of an increasing demand for small area statistics. Basic area level and unit level models have been studied in the literature to obtain empirical best linear unbiased predictors for small area means. Although this classical method is useful for estimating the small area means efficiently under strict model assumptions, it can be highly influenced by the presence of outliers in the data. In this article, the authors investigate the robustness properties of the classical estimators and propose a resistant method for small area estimation, which is useful for downweighting any influential observations in the data when estimating the model parameters. Simulations are carried out to study the behavior of the robust estimators in the presence of outliers, and these estimators are also compared to the ordinary classical estimators. To estimate the mean squared errors of the robust estimators of small area means, a parametric bootstrap method is adopted here, which is applicable to the unit level models with block diagonal covariance structures. Performance of the bootstrap mean squared error estimator is also investigated in the simulation study. The proposed robust method is also applied to some real life data, referred to as the survey and satellite data, obtained from a study described in a statistical journal.