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.
Notice that by simply plugging in the estimated parameter into the predictor, additional variability is unaccounted for, leading to overly optimistic prediction variances for the EBLUP.
[citation needed] Best linear unbiased predictions are similar to empirical Bayes estimates of random effects in linear mixed models, except that in the latter case, where weights depend on unknown values of components of variance, these unknown variances are replaced by sample-based estimates.
His work assisted the development of the selection index (SI) and estimated breeding value (EBV).
These statistical methods influenced the artificial insemination stud rankings used in the United States.
These early statistical methods are confused with the BLUP now common in livestock breeding.
The actual term BLUP originated out of work at the University of Guelph in Canada by Daniel Sorensen and Brian Kennedy, in which they extended Henderson's results to a model that includes several cycles of selection.
Further work by the University showed BLUP's superiority over EBV and SI leading to it becoming the primary genetic predictor[citation needed].
There is thus confusion between the BLUP model popularized above with the best linear unbiased prediction statistical method which was too theoretical for general use.