The Origin of BLUP and MME

07 March 2015

The origin of mixed model equations appears in two abstracts published by Henderson (1949, 1950). The formal proof that beta and u in Henderson (1949, 1950) are BLUE and BLUP is given in Henderson et al. (1959) and Henderson (1963), respectively. The latter was published in 1963 but actually given in 1961. Goldberger (1962) was the first to use the term “best linear unbiased predictor”. The acronym “BLUP” was coined by Henderson (1973). I obtained a copy of Henderson (1949, 1950, 1963) from my colleague Dr. Dale Van Vleck at UNL.

Henderson CR. (1949). Estimation of changes in herd environment. J Dairy Sci. (Abstract) 32: 706. [PDF]
Henderson CR. (1950). Estimation of genetic parameters. Ann Math Stat. (Abstract) 21: 309-310. [PDF]
Henderson CR, Kempthorne O, Searle SR, and Von Krosigk CM. (1959). The Estimation of environmental and genetic trends from records subject to culling. Biometrics 15: 192–218.
Henderson CR. (1963). Selection index and expected genetic advance. In Statistical Genetics and Plant Breeding 141-163. NAS-NRC 982, Washington, DC. [PDF]
Goldberger AS. (1962). Best linear unbiased prediction in the generalized linear regression model. J Am Statis Ass. 57: 369-375
Henderson CR. (1973). Sire evaluation and genetic trends. In Proceedings of the Animal Breeding and Genetics Symposium in Honour of Dr.Jay L. Lush 10-41. ASAS and ADSA, Champaign, Ill.

Also see this correspondence between Daniel Gianola and Andrew Gelman.