# Best linear unbiased prediction

Best linear unbiased prediction

In statistics, best linear unbiased prediction (BLUP) is used in linear mixed models for the prediction of random effects. Best linear unbiased predictions (BLUPs) of random effects are equivalent to best linear unbiased estimates (BLUEs) (see Gauss-Markov theorem) of fixed effects. The distinction arises because it is conventional to talk about "estimating" fixed effects but "predicting" random effects, but the two terms are otherwise equivalent. BLUP is used in animal breeding to estimate genetic merits.

Best linear unbiased predictions are the same as empirical Bayes estimates of random effects in linear mixed models.

References

*cite journal
author = Robinson, G.K.
year = 1991
title = That BLUP is a Good Thing: The Estimation of Random Effects
journal = Statistical Science
volume = 6
issue = 1
pages = 15–32
doi = 10.1214/ss/1177011926

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