= Best linear unbiased estimator
= BLUE
{c}
{synonym}
A best linear unbiased estimator minimizes <covariance> among linear estimators unbiased for the same target. In $Y=X\beta+\varepsilon$, assume $\mathbb E\varepsilon=0$, $X$ is a full-column-rank <design matrix> and the known <covariance matrix> $\Sigma$ is a <positive-definite matrix>. The <best linear unbiased estimator> of the coefficient vector is $(X^T\Sigma^{-1}X)^{-1}X^T\Sigma^{-1}Y$. A spatial trend estimate excludes the correlated residual prediction included in <universal kriging>.
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