Optimal linear Bayes and empirical Bayes estimation and prediction of the finite population mean

Rohana J. Karunamuni, Shunpu Zhang

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this article we investigate the estimation problem of the population mean of a finite population. Both point and interval estimators are of interest from Bayes and empirical Bayes point of views. Empirical Bayes analysis is concerned with the 'current' population mean, say γm, when the sample data are available from other similar (m-1) finite populations, Y1,..., Ym-1, as well as the data from the current population, Ym, where Yi = (Yi1,..., Yini), i = 1,..., m. Previous results on inference of γm have assumed either a normal model or a posterior linearity condition in making Bayes inference which is the kernel of the empirical Bayes problem. They resulted in examination of linear estimators of the sample mean Ȳm = nm-1j=1nm Ymj. In this paper, we propose to investigate a generalizing idea which generates optimal linear Bayes estimators of γm as functions of Ȳm. We develop optimal linear Bayes estimators of γm under two Bayesian models. They are optimal in the sense of minimizing the mean squared error with respect to the underlying models. The corresponding empirical Bayes analogues are obtained by replacing the unknown hyperparameters by their respective consistent estimates as usual. The asymptotic optimality criterion is employed in order to measure the goodness of the proposed empirical Bayes estimators. Very promising Bayes and empirical Bayes two-sided confidence intervals and predictors of γm are also discussed. A Monte Carlo study is conducted to evaluate the performance of the proposed estimators.

Original languageEnglish (US)
Pages (from-to)505-525
Number of pages21
JournalJournal of Statistical Planning and Inference
Volume113
Issue number2
DOIs
StatePublished - May 1 2003

Fingerprint

Empirical Bayes Estimation
Empirical Bayes
Finite Population
Bayes
Linear Estimator
Prediction
Bayes Estimator
Empirical Bayes Estimator
Estimator
Asymptotic Optimality
Consistent Estimates
Hyperparameters
Sample mean
Optimality Criteria
Bayesian Model
Monte Carlo Study
Mean Squared Error
Linearity
Confidence interval
Predictors

Keywords

  • Asymptotic optimality
  • Bayes estimators
  • Empirical Bayes
  • Finite populations
  • Linear estimators

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Cite this

Optimal linear Bayes and empirical Bayes estimation and prediction of the finite population mean. / Karunamuni, Rohana J.; Zhang, Shunpu.

In: Journal of Statistical Planning and Inference, Vol. 113, No. 2, 01.05.2003, p. 505-525.

Research output: Contribution to journalArticle

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