We consider estimation of a multivariate normal mean under
sum of squared error loss. We construct the efficiency bound (the lowest
achievable risk) for minimax shrinkage estimation. This
allows us to compare the regret of existing shrinkage estimators. We also
construct a new shrinkage estimator which achieves substantially lower maximum
regret than existing estimators.
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Some
of the above material is based upon work supported by the National Science
Foundation under Grant No. SES-0550908. Any opinions,
findings, and conclusions, or recommendations expressed in this material are
those of the author(s), and do not necessarily reflect the views of the NSF.