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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Published in | Econometric theory Vol. 31; no. 4; pp. 860 - 879 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
New York, USA
Cambridge University Press
01.08.2015
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Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 0266-4666 1469-4360 |
DOI: | 10.1017/S0266466614000693 |