12,000

We have over 12,000 students, from over 100 countries, within one of the safest campuses in the UK

93%

93% of Lancaster students go into work or further study within six months of graduating

Home > Research > Publications & Outputs > Empirical Bayes estimation of finite population...
View graph of relations

« Back

Empirical Bayes estimation of finite population means from complex surveys

Research output: Contribution to journalJournal article

Published

Journal publication date1997
JournalJournal of the American Statistical Association
Journal number440
Volume92
Number of pages8
Pages1555-1562
Original languageEnglish

Abstract

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 Robbins. The proposed empirical Bayes estimators are also compared to the classical regression estimators in terms of the relative savings loss due to Efron and Morris. 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.