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Datta, Gauri Sankar; Ghosh, Malay

Hierarchical Bayes estimators of the error variance in one-way ANOVA models. (English) Zbl 0822.62016

J. Stat. Plann. Inference 45, No. 3, 399-411 (1995).
Summary: For estimating the error variance in the one-way ANOVA problem, the paper proposes a class of hierarchical Bayes (HB) estimators which overcomes the Neyman-Scott problem. A subclass of these HB estimators is found to be minimax. The resulting class of priors is strictly contained within the class of HB priors which meets Peers’s criterion [H. W. Peers, J. R. Stat. Soc., Ser. B 27, 9-16 (1965; Zbl 0144.414)] of matching asymptotically the posterior probability of a credible set and the frequentist probability up to a certain order.

Cited in 4 Documents

MSC:

62F15 Bayesian inference
62J10 Analysis of variance and covariance (ANOVA)
62C20 Minimax procedures in statistical decision theory
62F10 Point estimation

Keywords:

hierarchical Bayes estimators; probability matching criterion; error variance; one-way ANOVA; Neyman-Scott problem; Peers’s criterion; posterior probability; credible set; frequentist probability

Citations:

Zbl 0144.414
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Full Text: DOI

References:

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