EMPIRICAL BAYES ESTIMATION OF FINITE POPULATION MEANS FROM COMPLEX SURVEYS

Estimation of finite population means is considered when samples are c ollected using a stratified sampling design. Finite populations for di fferent strata are assumed to be realizations from different superpopu lations. The true means of the observations lie on a regression surfac e with random intercepts for different strata. The true sampling varia nces are also different and random for different strata. The strata ar e connected through two common prior distributions, one for the interc epts and another for the sampling variances for all the strata. The mo del is appropriate in two important survey situations; First, it can b e applied to repeated surveys where the physical characteristics of th e sampling units change slowly over time. Second, the model is appropr iate in small-area estimation problems where a very few samples are av ailable for any particular area. Empirical Bayes estimators of the fin ite population means are shown to be asymptotically optimal in the sen se of Robbins. The proposed empirical Bayes estimators are also compar ed to the classical regression estimators in terms of the relative sav ings loss due to Efron and Morris. A measure of variability of the pro posed empirical Bayes estimator is considered based on bootstrap sampl es. This measure of Variability incorporates all sources of variations due to the estimation of various model parameters.