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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.
asymptotic minimaxity, Bayesian prediction, empirical Bayes, inadmissibility, multiple shrinkage, prior distributions, superharmonic marginals, unbiased estimates of risk
George, E. I., Liang, F., & Xu, X. (2012). From Minimax Shrinkage Estimation to Minimax Shrinkage Prediction. Statistical Science, 27 (1), 82-94. http://dx.doi.org/10.1214/11-STS383
Date Posted: 27 November 2017
This document has been peer reviewed.