Alternative mean square error estimators and confidence intervals for small area prediction under general designs

Abstract Estimating the mean square error of a small area predictor under an informative sampling design is a challenging problem. Existing approaches rely on approximations that have not been justified theoretically. We provide rigorous support for a mean square error estimator that is applicable to an informative sample design. The procedure can be used in combination with predictors of general parameters that may be nonlinear functions of the model response variable. We also construct calibrated prediction intervals that rely less on normality than standard prediction intervals. We validate the proposed measures of uncertainty through simulation. We apply the methods to predict several functions of sheet and rill erosion for Iowa counties using data from a complex agricultural survey.