Best linear unbiased prediction in the context of "Charles Roy Henderson"

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⭐ Core Definition: Best linear unbiased prediction

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 about 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.

In practice, it is often the case that the parameters associated with the random effect(s) term(s) are unknown; these parameters are the variances of the random effects and residuals. Typically the parameters are estimated and plugged into the predictor, leading to the empirical best linear unbiased predictor (EBLUP). 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.

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👉 Best linear unbiased prediction in the context of Charles Roy Henderson

Charles Roy Henderson ((1911-04-01)April 1, 1911 – (1989-03-14)March 14, 1989) was an American statistician and a pioneer in animal breeding — the application of quantitative methods for the genetic evaluation of domestic livestock. This is critically important because it allows farmers and geneticists to predict whether a crop or animal will have a desired trait, and to what extent the trait will be expressed. He developed mixed model equations to obtain best linear unbiased predictions of breeding values and, in general, any random effect. He invented three methods for the estimation of variance components in unbalanced settings of mixed models, and invented a method for constructing the inverse of Wright's numerator relationship matrix based on a simple list of pedigree information. He, with his Ph.D. student Shayle R. Searle, greatly extended the use of matrix notation in statistics. His methods are widely used by the domestic livestock industry throughout the world and are a cornerstone of linear model theory.

Henderson obtained his B.Sc., M.Sc.(nutrition) and Ph.D.(breeding) degrees at Iowa State University, where he was a student of Professor L. N. Hazel. Henderson joined the faculty of the Department of Animal Science at Cornell University in 1948 and headed the Animal Breeding division for nearly 30 years until he retired in 1976. After retiring from Cornell, he was a visiting professor at the University of Guelph and University of Illinois until his death. He completed his book in 1984 at the University of Guelph.

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Best linear unbiased prediction in the context of Kriging

In statistics, originally in geostatistics, kriging or Kriging (/ˈkriːɡɪŋ/), also known as Gaussian process regression, is a method of interpolation based on Gaussian process governed by prior covariances. Under suitable assumptions of the prior, kriging gives the best linear unbiased prediction (BLUP) at unsampled locations. Interpolating methods based on other criteria such as smoothness (e.g., smoothing spline) may not yield the BLUP. The method is widely used in the domain of spatial analysis and computer experiments. The technique is also known as Wiener–Kolmogorov prediction, after Norbert Wiener and Andrey Kolmogorov.

The theoretical basis for the method was developed by the French mathematician Georges Matheron in 1960, based on the master's thesis of Danie G. Krige, the pioneering plotter of distance-weighted average gold grades at the Witwatersrand reef complex in South Africa. Krige sought to estimate the most likely distribution of gold based on samples from a few boreholes. The English verb is to krige, and the most common noun is kriging. The word is sometimes capitalized as Kriging in the literature.

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Best linear unbiased prediction in the context of Animal breeding

Animal breeding is a branch of animal science that addresses the evaluation (using best linear unbiased prediction and other methods) of the genetic value (estimated breeding value, EBV) of livestock. Selecting for breeding animals with superior EBV in growth rate, egg, meat, milk, or wool production, or with other desirable traits has revolutionized livestock production throughout the entire world. The scientific theory of animal breeding incorporates population genetics, quantitative genetics, statistics, and recently molecular genetics and is based on the pioneering work of Sewall Wright, Jay Lush, and Charles Henderson.

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LINKED FROM (PARENTS)
← Kriging ← Animal breeding ← Charles Roy Henderson
LINKS TO (CHILDREN)
Statistics → Mixed model → Random effects model → Charles Roy Henderson → Gauss–Markov theorem →