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February 2012 From Minimax Shrinkage Estimation to Minimax Shrinkage Prediction
Edward I. George, Feng Liang, Xinyi Xu
Statist. Sci. 27(1): 82-94 (February 2012). DOI: 10.1214/11-STS383


In a remarkable series of papers beginning in 1956, Charles Stein set the stage for the future development of minimax shrinkage estimators of a multivariate normal mean under quadratic loss. More recently, parallel developments have seen the emergence of minimax shrinkage estimators of multivariate normal predictive densities under Kullback–Leibler risk. We here describe these parallels emphasizing the focus on Bayes procedures and the derivation of the superharmonic conditions for minimaxity as well as further developments of new minimax shrinkage predictive density estimators including multiple shrinkage estimators, empirical Bayes estimators, normal linear model regression estimators and nonparametric regression estimators.


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Edward I. George. Feng Liang. Xinyi Xu. "From Minimax Shrinkage Estimation to Minimax Shrinkage Prediction." Statist. Sci. 27 (1) 82 - 94, February 2012.


Published: February 2012
First available in Project Euclid: 14 March 2012

zbMATH: 1330.62288
MathSciNet: MR2953497
Digital Object Identifier: 10.1214/11-STS383

Rights: Copyright © 2012 Institute of Mathematical Statistics


Vol.27 • No. 1 • February 2012
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