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SHRINKAGE EFFICIENCY BOUNDS

Published online by Cambridge University Press:  02 October 2014

Bruce E. Hansen
Bruce E. Hansen*
Affiliation:
University of Wisconsin
*
*Address correspondence to Bruce Hansen, Department of Economics, 1180 Observatory Drive, University of Wisconsin, Madison, WI 53706, USA; e-mail: behansen@wisc.edu.
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Abstract

This paper is an extension of Magnus (2002, Econometrics Journal 5, 225–236) to multiple dimensions. 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 in the class of minimax orthogonally invariate estimators satisfying the sufficient conditions of Efron and Morris (1976, Annals of Statistics 4, 11–21). This allows us to compare the regret of existing orthogonally invariate shrinkage estimators. We also construct a new shrinkage estimator which achieves substantially lower maximum regret than existing estimators.

Type
ARTICLES
Information
Econometric Theory , Volume 31 , Issue 4 , August 2015 , pp. 860 - 879
Copyright
Copyright © Cambridge University Press 2014 

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Footnotes

Research supported by the National Science Foundation. I thank a referee for a thorough reading of the paper and helpful comments.

References

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