On parametric bootstrap methods for small area prediction

TL;DR: In this article, a bias-corrected mean-squared error estimator for small area prediction is proposed. But this estimator is limited to a narrow range of models, and it is not applicable to general two-level models.

Abstract: Summary. The particularly wide range of applications of small area prediction, e.g. in policy making decisions, has meant that this topic has received substantial attention in recent years. The problems of estimating mean-squared predictive error, of correcting that estimator for bias and of constructing prediction intervals have been addressed by various workers, although existing methodology is still restricted to a narrow range of models. To overcome this difficulty we develop new, bootstrap-based methods, which are applicable in very general settings, for constructing bias-corrected estimators of mean-squared error and for computing prediction regions. Unlike existing techniques, which are based largely on Taylor expansions, our bias-corrected mean-squared error estimators do not require analytical calculation. They also have the property that they are non-negative. Our prediction intervals have a high degree of coverage accuracy, O(n−3), where n is the number of areas, if double-bootstrap methods are employed. The techniques do not depend on the form of the small area estimator and are applicable to general two-level, small area models, where the variables at either level can be discrete or continuous and, in particular, can be non-normal. Most importantly, the new methods are simple and easy to apply.