In
statistics,
best linear unbiased prediction (
BLUP) is used in linear
mixed models for the estimation of
random effects. BLUP was derived by
Charles Roy Henderson in 1950 but the term "best linear unbiased predictor" (or "prediction") seems not to have been used until 1962. "Best linear unbiased predictions" (BLUPs) of random effects are similar 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. (This is a bit strange since the random effects have already been "realized"; they already exist. The use of the term "prediction" may be because in the field of animal breeding in which Henderson worked, the random effects were usually genetic merit, which could be used to predict the quality of offspring (Robinson page 28)). However, the equations for the "fixed" effects and for the random effects are different.