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;
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.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11587/472119
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 17
  • ???jsp.display-item.citation.isi??? 15
social impact