Empirical Bayes estimation of finite population means from complex surveys.

*(English)*Zbl 0912.62012Summary: Estimation of finite population means is considered when samples are collected using a stratified sampling design. Finite populations for different strata are assumed to be realizations from different superpopulations. The true means of the observations lie on a regression surface with random intercepts for different strata. The true sampling variances are also different and random for different strata. The strata are connected through two common prior distributions, one for the intercepts and another for the sampling variances for all the strata. The model is appropriate in two important survey situations. First, it can be applied to repeated surveys where the physical characteristics of the sampling units change slowly over time. Second, the model is appropriate in small-area estimation problems where a very few samples are available for any particular area.

Empirical Bayes estimators of the finite population means are shown to be asymptotically optimal in the sense of H. Robbins [Proc. 3rd Berkeley Sympos. Math. Statist. Probability 1, 157-163 (1956; Zbl 0074.35302)]. The proposed empirical Bayes estimators are also compared to the classical regression estimators in terms of the relative savings loss due to B. Efron and C. Morris [J. Am. Stat. Assoc. 68, 117-130 (1973; Zbl 0275.62005)]. A measure of variability of the proposed empirical Bayes estimator is considered based on bootstrap samples. This measure of variability incorporates all sources of variations due to the estimation of various model parameters. A numerical study is conducted to evaluate the performance of the proposed empirical Bayes estimator compared to rival estimators.

Empirical Bayes estimators of the finite population means are shown to be asymptotically optimal in the sense of H. Robbins [Proc. 3rd Berkeley Sympos. Math. Statist. Probability 1, 157-163 (1956; Zbl 0074.35302)]. The proposed empirical Bayes estimators are also compared to the classical regression estimators in terms of the relative savings loss due to B. Efron and C. Morris [J. Am. Stat. Assoc. 68, 117-130 (1973; Zbl 0275.62005)]. A measure of variability of the proposed empirical Bayes estimator is considered based on bootstrap samples. This measure of variability incorporates all sources of variations due to the estimation of various model parameters. A numerical study is conducted to evaluate the performance of the proposed empirical Bayes estimator compared to rival estimators.