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

An empirical Bayes derivation of best linear unbiased predictors

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

Received 8 October 2001

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.