Estimation of the prediction mean square error (MSE) in SAE under the frequentist approach is known to be a complicated problem even under well defined models because of the use of estimated model parameters for the predictors and the fact that the added variability implied by this cannot be ignored.
Estimation of the prediction MSE is particularly difficult when the response variable is binary and the existing resampling methods like the jackknife and double-bootstrap often produce unsatisfactory estimates. In this research which was part of a PhD dissertation by Dr. Solange Correa from Brasil under the supervision of Professors Chris Skinner and Danny Pfeffermann, a new general method for bootstrap bias corrections is developed, and then applied to the estimation of prediction MSE in SAE with binary data. Simulation results using a unit level mixed logistic model indicate the better performance of the proposed estimators compared to the other existing methods.
A paper summarizing the results of this study is in the final stages of preparation.
Small area estimation with state-space models subject to benchmark constraints.