Mean Square Error Estimation of Small Area Predictors by Use of Parametric and Nonparametric Bootstrap

In this article, we propose and compare some old and new parametric and nonparametric bootstrap methods for MSE estimation in small area estimation, restricting to the case of the widely used Fay-Herriot model. The parametric method consists of generating parametrically a large number of area bootstrap samples from the model fitted to the original data, re-estimating the model parameters for each bootstrap sample and then estimating the separate components of the MSE. The use of double-bootstrap is also considered. The nonparametric method generates the samples by bootstrapping standardized residuals, estimated from the original sample data. The bootstrap procedures are compared to other methods proposed in the literature in a simulation study, which also examines the robustness of the various methods to non-normality of the model error terms. A design-based MSE estimator for the Fay-Herriot model-dependent predictor is also described and its performance is investigated in a separate simulation study. AMS subject classification: 62F10, 62F40