Sankhya: The Indian Journal of Statistics

1999, Volume 61, Series B, Pt. 2, pp. 305-314

EMPIRICAL BAYES ESTIMATION OF FINITE POPULATION VARIANCES

By

FERRY BUTAR BUTAR, Sam Houston State University, Huntsville, Texas

and

P. LAHIRI, University of Nebraska, Lincoln

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 approximation 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.

AMS (1991) subject classification. 62C10.

Key words and phrases. Bootstrap, Laplace approximation, monte carlo.

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