Empirical Bayes estimation in finite population sampling under functional measurement error models

Malay Ghosh, Karabi Sinha

Research output: Contribution to journalArticle

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Abstract

The paper considers simultaneous estimation of finite population means for several strata. A model-based approach is taken, where the covariates in the super-population model are subject to measurement errors. Empirical Bayes (EB) estimators of the strata means are developed and an asymptotic expression for the MSE of the EB estimators is provided. It is shown that the proposed EB estimators are "first order optimal" in the sense of Robbins [1956. An empirical Bayes approach to statistics. In: Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, University of California Press, Berkeley, pp. 157-164], while the regular EB estimators which ignore the measurement error are not.

Original languageEnglish
Pages (from-to)2759-2773
Number of pages15
JournalJournal of Statistical Planning and Inference
Volume137
Issue number9
DOIs
StatePublished - 1 Sep 2007

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Keywords

  • Asymptotic optimality
  • Bayes risk
  • Consistency

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