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Media type:
E-Article
Title:
SHRINKAGE EFFICIENCY BOUNDS
Contributor:
Hansen, Bruce E.
imprint:
Cambridge University Press (CUP), 2015
Published in:Econometric Theory
Language:
English
DOI:
10.1017/s0266466614000693
ISSN:
0266-4666;
1469-4360
Origination:
Footnote:
Description:
<jats:p>This paper is an extension of Magnus (2002, <jats:italic>Econometrics Journal</jats:italic> 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, <jats:italic>Annals of Statistics</jats:italic> 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.</jats:p>