Empirical and hierarchical Bayes competitors of preliminary test estimators in two sample problems

DOI10.1016/0047-259X(88)90126-1zbMath0665.62053OpenAlexW1977007757MaRDI QIDQ1116232

Malay Ghosh, Bimal Kumar Sinha

Publication date: 1988

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0047-259x(88)90126-1

zbMATH Keywords

A sample from the distribution \(N_ p(\mu _ 1,\sigma ^ 2V_ 1)\), and a sample from \(N_ p(\mu _ 2,\sigma ^ 2V_ 2)\) are given, and the problem is to estimate \(\mu _ 1\) using also the second sample if \(\mu _ 2\) is supposed to be close to \(\mu _ 1\). In the formal statement of the problem it is assumed that prior distributions of \(\mu _ 1\) and \(\mu _ 2\) are normal with a common mean, and Bayesian estimatorsBayes riskpreliminary test estimatorfrequentist riskempirical Bayes estimatorhierarchical Bayes estimator

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Point estimation (62F10) Empirical decision procedures; empirical Bayes procedures (62C12)

Related Items (5)

Shrinkage estimation of a mean vector in a two-sample problem ⋮ Bayesian simultaneous estimation for means in \(k\)-sample problems ⋮ On the near equivalence of the testimation and Schwarz information criterion (SIC) to study Cepheid period-luminosity relation ⋮ Hierarchical empirical Bayes estimation of two sample means under divergence loss ⋮ Bayes minimax competitors of preliminary test estimators in \(k\) sample problems

Cites Work

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• Estimation of the mean of a multivariate normal distribution
• Proper Bayes minimax estimators of the multivariate normal mean vector for the case of common unknown variances
• Stein's Estimation Rule and Its Competitors--An Empirical Bayes Approach
• Proper Bayes Minimax Estimators of the Multivariate Normal Mean
• Non-Optimality of Preliminary-Test Estimators for the Mean of a Multivariate Normal Distribution

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