An empirical bayes derivation of best linear unbiased predictors

Abstract

Let (Y1,θ1),..., (Yn,θn) be independent real-valued random vectors with Yi, given θi, is distributed according to a distribution depending only on θi for i=1,...,n. In this paper, best linear unbiased predictors (BLUPs) of the θi's are investigated. We show that BLUPs of θi's do not exist in certain situations. Furthermore, we present a general empirical Bayes technique for deriving BLUPs. Copyright © 2002 Hindawi Publishing Corporation. All rights reserved.