International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 12, Pages 703-714
doi:10.1155/S016117120211009X

An empirical Bayes derivation of best linear unbiased predictors

Rohana J. Karunamuni

Department of Mathematical and Statistical Sciences, University of Alberta, Alberta, Edmonton T6G 2G1, Canada

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.