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Which is the best linear unbiased prediction method?
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.
Is the BLUP problem a linear or unbiased problem?
The BLUP problem of providing an estimate of the observation-error-free value for the k th observation, can be formulated as requiring that the coefficients of a linear predictor, defined as should be chosen so as to minimise the variance of the prediction error, subject to the condition that the predictor is unbiased,
What do you need to know about simple linear regression?
Simple linear regression analysis. • Linear relationship between x (explanatory variable) and y (dependent variable) • Epsilon describes the random component of the linear relationship between x and y.
Why do we use prediction in animal breeding?
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.
Which is the best linear unbiased estimate blue or Blup?
BLUP vs BLUE. In contrast to the case of best linear unbiased estimation, the “quantity to be estimated”, , not only has a contribution from a random element but one of the observed quantities, specifically which contributes to , also has a contribution from this same random element. In contrast to BLUE, BLUP takes into account known…
Which is the best linear unbiased predictor of BV 2?
Almost all animal breeding is based on such models, with REML(restricted max likelihood) used to estimated variances and BLUP (best linear unbiased predictors) used to predict BV 2 BLUP in plant breeding BLUP has migrated from animal breedinginto plant breeding.
How is Blup used as a shrinkage estimator?
BLUP is a shrinkage estimator For a single observation on one individual,BLUP(a) = h2(y-µ) The difference between the observed value (y)and the mean (µ) is shrunk by the factor h2 —shrinks the estimate back towards the mean(zero in the case of BVs) More generally, BLUP(a) = GZTV-1(y- X)