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 not about estimating fixed effects but rather 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 w
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| - Best linear unbiased prediction (en)
- BLUE (sv)
- 最佳线性无偏预测 (zh)
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| - BLUE är en engelsk akronym för Best Linear Unbiased Estimator, vilket betyder ungefär "den linjära funktion som bäst approximerar data utan snedvridning". Inom regressionsanalysen visar man att minsta kvadratmetoden garanterar denna egenskap. BLUP härleddes av Charles Roy Henderson 1950, men termen "best linear unbiased predictor" verkar inte ha använts förrän 1962. Termen BLUP har sitt ursprung i arbetet vid University of Guelph i Kanada av Daniel Sorensen och Brian Kennedy, där de utökade Hendersons resultat till en modell som inkluderar flera urvalscykler. (sv)
- 最佳线性无偏预测(best linear unbiased prediction， 简称BLUP)，又音译为“布拉普”，是统计学上用于线性混合模型对进行预测的一种方法。最佳线性无偏预测由提出。随机效应的最佳线性无偏预测（BLUP）等同于固定效应的最佳线性无偏估计（best linear unbiased estimates, BLUE）（参见高斯-马尔可夫定理）。因为对固定效应使用估计一词，而对随机效应使用预测，这两个术语基本是等同的。BLUP被大量使用于动物育种。 最佳线性无偏预测和线性混合模型中随机效应的相同。 (zh)
- 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 not about estimating fixed effects but rather 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 w (en)
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| - 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 not about estimating fixed effects but rather 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 (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. 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. (en)
- BLUE är en engelsk akronym för Best Linear Unbiased Estimator, vilket betyder ungefär "den linjära funktion som bäst approximerar data utan snedvridning". Inom regressionsanalysen visar man att minsta kvadratmetoden garanterar denna egenskap. BLUP härleddes av Charles Roy Henderson 1950, men termen "best linear unbiased predictor" verkar inte ha använts förrän 1962. Termen BLUP har sitt ursprung i arbetet vid University of Guelph i Kanada av Daniel Sorensen och Brian Kennedy, där de utökade Hendersons resultat till en modell som inkluderar flera urvalscykler. (sv)
- 最佳线性无偏预测(best linear unbiased prediction， 简称BLUP)，又音译为“布拉普”，是统计学上用于线性混合模型对进行预测的一种方法。最佳线性无偏预测由提出。随机效应的最佳线性无偏预测（BLUP）等同于固定效应的最佳线性无偏估计（best linear unbiased estimates, BLUE）（参见高斯-马尔可夫定理）。因为对固定效应使用估计一词，而对随机效应使用预测，这两个术语基本是等同的。BLUP被大量使用于动物育种。 最佳线性无偏预测和线性混合模型中随机效应的相同。 (zh)
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