  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.
