SHRINKAGE EFFICIENCY BOUNDS

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 m...

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Bibliographic Details
Published inEconometric theory Vol. 31; no. 4; pp. 860 - 879
Main Author Hansen, Bruce E.
Format Journal Article
LanguageEnglish
Published New York, USA Cambridge University Press 01.08.2015
Subjects
Econometrics
Efficiency
Estimates
Estimating techniques
Random variables
Shrinkage
Statistical analysis
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Summary: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.
ISSN:0266-4666
1469-4360
DOI:10.1017/S0266466614000693