Abstract :
Suppose we observe X ; Nm~Ab,s2I ! and would like to estimate the predictive
density p~ y6b! of a future Y;Nn~Bb,s2I !+ Evaluating predictive estimates p[ ~ y6x!
by Kullback–Leibler loss, we develop and evaluate Bayes procedures for this problem+
We obtain general sufficient conditions for minimaxity and dominance of
the “noninformative” uniform prior Bayes procedure+ We extend these results to
situations where only a subset of the predictors in A is thought to be potentially
irrelevant+We then consider the more realistic situation where there is model uncertainty
and this subset is unknown+ For this situation we develop multiple shrinkage
predictive estimators and obtain general minimaxity and dominance conditions+
Finally, we provide an explicit example of a minimax multiple shrinkage predictive
estimator based on scaled harmonic priors+
