The Annals of Statistics

Bayesian Prediction in Linear Models: Applications to Small Area Estimation

Gauri Sankar Datta and Malay Ghosh

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This paper introduces a hierarchical Bayes (HB) approach for prediction in general mixed linear models. The results find application in small area estimation. Our model unifies and extends a number of models previously considered in this area. Computational formulas for obtaining the Bayes predictors and their standard errors are given in the general case. The methods are applied to two actual data sets. Also, in a special case, the HB predictors are shown to possess some interesting frequentist properties.

Article information

Ann. Statist., Volume 19, Number 4 (1991), 1748-1770.

First available in Project Euclid: 12 April 2007

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Primary: 62D05: Sampling theory, sample surveys
Secondary: 62F11 62F15: Bayesian inference 62J99: None of the above, but in this section

Hierarchical Bayes empirical Bayes mixed linear models best linear unbiased prediction best unbiased prediction small area estimation nested error regression model random regression coefficients model two-stage sampling elliptically symmetric distributions


Datta, Gauri Sankar; Ghosh, Malay. Bayesian Prediction in Linear Models: Applications to Small Area Estimation. Ann. Statist. 19 (1991), no. 4, 1748--1770. doi:10.1214/aos/1176348369.

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