EMPIRICAL BAYES ESTIMATION OF FINITE POPULATION VARIANCES

SUMMARY. The Kleffe-Rao model, a mixed model with random sampling variances, is extended to produce empirical Bayes estimators of several finite population variances. The proposed empirical Bayes estimators do not have a closed form. A second order Laplace ap-proximation is used which works well for moderately large sample sizes. This approximation is specially useful when the uncertainties of the proposed empirical Bayes estimators are measured by the parametric bootstrap technique. A numerical example is considered to demonstrate the method. 1