Bruce E. Hansen

“Shrinkage Efficiency Bounds,” Econometric Theory, (2015), 31, 860-879.


This paper is an extension of Magnus (2002) 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 estimators satisfying the sufficient conditions of Efron and Morris (1976). 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.