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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. [1] "
Under suitable assumptions of the prior, kriging gives the best linear unbiased prediction (BLUP) at unsampled locations. [1] 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.
Regression-kriging is an implementation of the best linear unbiased predictor (BLUP) for spatial data, i.e. the best linear interpolator assuming the universal model of spatial variation. Matheron (1969) proposed that a value of a target variable at some location can be modeled as a sum of the deterministic and stochastic components: [2]
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 ...
The solutions to the MME, ^ and ^ are best linear unbiased estimates and predictors for and , respectively. This is a consequence of the Gauss–Markov theorem when the conditional variance of the outcome is not scalable to the identity matrix.
In statistics, the Gauss–Markov theorem (or simply Gauss theorem for some authors) [1] states that the ordinary least squares (OLS) estimator has the lowest sampling variance within the class of linear unbiased estimators, if the errors in the linear regression model are uncorrelated, have equal variances and expectation value of zero. [2]
Economics is known as the "dismal science" -- an often-grim analysis of numbers and trends that reveals the hidden workings of society. But when it comes to making predictions about the future ...
Best linear unbiased estimator, also known as the Gauss–Markov theorem states that the ordinary least squares (OLS) estimator has the lowest sampling variance within the class of linear unbiased estimators, if the errors in the linear regression model are uncorrelated, have equal variances and expectation value of zero. [11]