Sankhya: The Indian Journal of Statistics
1994, Volume 56, Series B, Pt. 3 , pp. 415 -- 433
FINITE POPULATION PREDICTION FOR STRATIFIED SAMPLING UNDER ERROR-IN-VARIABLES SUPERPOPULATION MODELS
MANAS K. CHATTOPADHYAY and GAURI S. DATTA, Gallup Organisation and University of Georgia
SUMMARY. This article considers simultaneous estimation of means from several strata under error-in-variables superpopulation model where variables are assumed to be measured with measurement error. We propose Bayes estimators for this problem, both hierarchical Bayes (HB) and empirical Bayes (EB). Our results find application in small area estimation where typically there are few observations from each individual stratum and simultaneous estimation of several strata means can be greatly improved by pooling information from similar neighbouring areas. The model formulated in this paper is different from models previously considered in this area in that none of them assumes measurement error. This model also extends Bolfarine's (1991) simple location error-in-variable superpopulation model to stratified sampling. Our results are applied to a real data set. A simulation study suggests that HB and EB estimators perform considerably better than the sample strata means, the traditional estimators.
AMS (1980) subject classification. 62D05.
Key words and phrases. Bayesian, empirical Bayes, hierarchical Bayes, measurement error, small area estimation.
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