= Correlated Gaussian common-mean estimator
{title2=$\widehat\mu=(\mathbf1^TC^{-1}X)/(\mathbf1^TC^{-1}\mathbf1)$}
For $X\sim N(\mu\mathbf1,C)$ with a known <positive-definite matrix> $C$, the <maximum-likelihood estimator> of $\mu$ is $\widehat\mu=(\mathbf1^TC^{-1}X)/(\mathbf1^TC^{-1}\mathbf1)$. It is unbiased with variance $(\mathbf1^TC^{-1}\mathbf1)^{-1}$, attaining the <Cramer-Rao bound>. It is also the best <linear unbiased estimator>. Pairwise admissible <correlation coefficients> alone do not ensure that $C$ is a valid <covariance matrix>; the entire matrix must be symmetric and a <positive semidefinite matrix>. Inverse-based formulas require positive definiteness.
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