We consider small area estimation under a nested error linear regression model with measurement errors in the covariates. We propose an objective Bayesian analysis of the model to estimate the finite population means of the small areas. In particular, we derive Jeffreys' prior for model parameters. We also show that Jeffreys' prior, which is improper, leads, under very general conditions, to a proper posterior distribution. We have also performed a simulation study where we have compared the Bayes estimates of the finite population means under the Jeffreys' prior with other Bayesian estimates obtained via the use of the standard flat prior and with non-Bayesian estimates, i.e., the corresponding empirical Bayes estimates and the direct estimates. © 2012 International Society for Bayesian Analysis.

We consider small area estimation under a nested error linear regression model with measurement errors in the covariates. We propose an objective Bayesian analysis of the model to estimate the finite population means of the small areas. In particular, we derive Jeffreys' prior for model parameters. We also show that Jeffreys' prior, which is improper, leads, under very general conditions, to a proper posterior distribution. We have also performed a simulation study where we have compared the Bayes estimates of the finite population means under the Jeffreys' prior with other Bayesian estimates obtained via the use of the standard flat prior and with non-Bayesian estimates, i.e., the corresponding empirical Bayes estimates and the direct estimates. © 2012 International Society for Bayesian Analysis.

Objective Bayesian Analysis of a Measurement Error Small Area Model / Arima, Serena; Gauri S., Datta; Liseo, Brunero. - In: BAYESIAN ANALYSIS. - ISSN 1936-0975. - ELETTRONICO. - 7:2(2012), pp. 363-383. [10.1214/12-ba712]

Objective Bayesian Analysis of a Measurement Error Small Area Model

ARIMA, SERENA;LISEO, Brunero
2012

Abstract

We consider small area estimation under a nested error linear regression model with measurement errors in the covariates. We propose an objective Bayesian analysis of the model to estimate the finite population means of the small areas. In particular, we derive Jeffreys' prior for model parameters. We also show that Jeffreys' prior, which is improper, leads, under very general conditions, to a proper posterior distribution. We have also performed a simulation study where we have compared the Bayes estimates of the finite population means under the Jeffreys' prior with other Bayesian estimates obtained via the use of the standard flat prior and with non-Bayesian estimates, i.e., the corresponding empirical Bayes estimates and the direct estimates. © 2012 International Society for Bayesian Analysis.
2012
We consider small area estimation under a nested error linear regression model with measurement errors in the covariates. We propose an objective Bayesian analysis of the model to estimate the finite population means of the small areas. In particular, we derive Jeffreys' prior for model parameters. We also show that Jeffreys' prior, which is improper, leads, under very general conditions, to a proper posterior distribution. We have also performed a simulation study where we have compared the Bayes estimates of the finite population means under the Jeffreys' prior with other Bayesian estimates obtained via the use of the standard flat prior and with non-Bayesian estimates, i.e., the corresponding empirical Bayes estimates and the direct estimates. © 2012 International Society for Bayesian Analysis.
jeffreys prior; bayesian inference; small area model; jeffreys' prior
01 Pubblicazione su rivista::01a Articolo in rivista
Objective Bayesian Analysis of a Measurement Error Small Area Model / Arima, Serena; Gauri S., Datta; Liseo, Brunero. - In: BAYESIAN ANALYSIS. - ISSN 1936-0975. - ELETTRONICO. - 7:2(2012), pp. 363-383. [10.1214/12-ba712]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/443818
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