Resampling-based empirical prediction: an application to small area estimation

Best linear unbiased prediction is well known for its wide range of applications including small area estimation. While the theory is well established for mixed linear models and under normality of the error and mixing distributions, the literature is sparse for nonlinear mixed models under nonnormality of the error distribution or of the mixing distributions. We develop a resampling-based unified approach for predicting mixed effects under a generalized mixed model set-up. Second-order-accurate nonnegative estimators of mean squared prediction errors are also developed. Given the parametric model, the proposed methodology automatically produces estimators of the small area parameters and their mean squared prediction errors, without requiring explicit analytical expressions for the mean squared prediction errors.