Dear Colleagues,
Yesterday I requested information on a paper by James & Stein from
many moons ago. My thanks to several respondents for the reference.
Some have emailed me asking for it, so here it is. I'm reproducing
below what Ted Harding sent me.
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No doubt the James-Stein paper in question is
James, W. and Stein, C. (1961). Estimation with quadratic loss.
Proc. Fourth Berkeley Symposium Prob & Math Stat, vol 1, pp 361-380.
In this they derived the "paradox" that, for a multivariate normal
distribution with a uniform (improper) prior distribution for the
means, the sample mean is not an admissible estimator (i.e. it can
be improved on) even though it is the "best Bayesian" estimator
(posterior mean) for that prior. This situation does not arise
if the prior for the means is proper: the posterior mean is
always admissible.
Quite probably the JRSS paper you are thinking of is
Lindley, D.V. and Smith, A.F.M. (1972). Bayes estimates for
the linear model. JRSS (B) vol 34, pp 1-41 (with discussion).
See especially the discussion for the sort of comment you refer to.
Robert Newcombe.
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