Abstract: The Bayes estimator of a small area mean is shown to have strictly smaller mean squared error (MSE) than that of the corresponding best linear unbiased predictor (BLUP) for the Kleffe-Rao model, an extended mixed model with random sampling variances. The model is then extended to incorporate sampling weights, covariances and unequal sample sizes. A hierarchical Bayesian procedure which takes into account various sources of variabilities has been proposed. A specific small area estimation problem using data from the U.S. Consumer Expenditure Survey is considered. Based on a robust (i.e., model free) evaluation criterion, the proposed hierarchical Bayes estimator turns out to be superior to both estimated BLUP and the direct survey estimators. The posterior variances which measure the accuracy of the hierarchical Bayes estimates are always smaller than the corresponding variances of the direct survey estimates. The current state of estimated BLUP theory is not rich enough to provide reliable estimates of the MSE of the estimated BLUP for the example considered in this article.
Key words and phrases: Adaptive rejection sampling, consumer expenditure, Gibbs sampling, integrated Bayes risk, mean squared error, sampling weight.