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.