We consider the problem of estimating a vector (µ1,...,µn) of normal means under a squared loss, based on independent Y_i ∼ N(µ_i,1), i = 1,...,n. We use ideas and techniques from non-parametric empirical Bayes, to obtain asymptotical risk improvement of classical shrinkage estimators, such as, Stein's estimator, Fay-Herriot, Kalman filter, and more. We consider both the sequential and retrospective estimation problems. We elaborate on state-space models and the Kalman filter estimators. The performance of our improving method is demonstrated both through simulations and real data examples.

Joint work with Ariel Mansura, and Ya'acov Ritov