From Minimax Shrinkage Estimation to Minimax Shrinkage Prediction

Details From Minimax Shrinkage Estimation to Minimax Shrinkage Prediction From Minimax Shrinkage Estimation to Minimax Shrinkage Prediction

2012-03-26

arxiv.org/abs/1203.5617v1

Statistical Science 2012, Vol. 27, No. 1, 82-94

Statistics

Methodology

Published in at http://dx.doi.org/10.1214/11-STS383 the Statistical Science (http://www.imstat.org/sts/) by the Institute of M

Scientific paper

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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