Abstract
In this paper, we consider the estimation of a mean vector of a multivariate normal population where the mean vector is suspected to be nearly equal to mean vectors of \(k-1\) other populations. As an alternative to the preliminary test estimator based on the test statistic for testing hypothesis of equal means, we derive empirical and hierarchical Bayes estimators which shrink the sample mean vector toward a pooled mean estimator given under the hypothesis. The minimaxity of those Bayesian estimators are shown, and their performances are investigated by simulation.
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Acknowledgements
We would like to thank the Editor, the Associate Editor and the reviewer for valuable comments and helpful suggestions which led to an improved version of this paper. Research of the second author was supported in part by Grant-in-Aid for Scientific Research (15H01943 and 26330036) from Japan Society for the Promotion of Science.
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Imai, R., Kubokawa, T. & Ghosh, M. Bayes minimax competitors of preliminary test estimators in k sample problems. Jpn J Stat Data Sci 1, 3–21 (2018). https://doi.org/10.1007/s42081-018-0002-x
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DOI: https://doi.org/10.1007/s42081-018-0002-x