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Biometrika 1972 59(3):693-695; doi:10.1093/biomet/59.3.693
© 1972 by Biometrika Trust
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MISCELLANEA

Shrinkage of the posterior mean In the normal case

R. L. ANDREWS, J. C. ARNOLD and R. G. KRTJTCHKOFF

Virginia Polytechnic Institute and State University

Bayes estimation with a normal conditional distribution and an unknown prior distribution is considered. It is shown that the posterior mean always shrinks the observation toward a local maximum of the marginal distribution of the observation. For any symmetric, unimodal prior distribution itis shown that the posterior mean lies between the observation and the prior mean.

Key Words: Bayes estimation for mean of normal distribution • Shrinkage of point estimates


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