On measures of uncertainty of empirical Bayes small-area estimators

Small area typically refers to a small geographic area or a demographic group for which very little information is obtained from the sample surveys. An empirical Bayes (EB) method uses sample survey data in conjunction with relevant supplementary data which are obtained from various administrative sources. The method has been found to be very useful in many applications of small-area estimation and related problems. In this paper, a method based on bootstrap samples is proposed to measure the accuracy of the proposed EB estimator of a small-area characteristic. A simple approximation of the method which does not require any bootstrap simulation is also proposed. The model expectation of the proposed measure of uncertainty of the EB estimator is equal to the integrated Bayes risk of the EB estimator up to the order O(m(-1)). Two well-known data sets are considered to compare the proposed method with some existing methods. A Monte Carlo simulation is conducted to compare the performances of different measures of uncertainty. (C) 2002 Elsevier Science B.V. All rights reserved.