An empirical Bayes derivation of best linear unbiased predictors (Q1848011)

Summary: Let \((Y_{1},\theta _{1}),\dots, (Y_{n},\theta_{n})\) be independent real-valued random vectors with \(Y_{i}\), given \(\theta_{i}\), distributed according to a distribution depending only on \(\theta_{i}\) for \(i=1,\dots,n\). Best linear unbiased predictors (BLUPs) of the \(\theta_i\)'s are investigated. We show that BLUPs of \(\theta_i\)'s do not exist in certain situations. Furthermore, we present a general empirical Bayes technique for deriving BLUPs.