Linear Model with Non-White Noise

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When the assumption that the noise $w$ is iid does not hold, and $\Sigma \ne {\sigma }^{2}I$ (Noise Covariance Matrix). The estimator is still MVU and efficient.

$$\hat{\Theta }=(H^T{\Sigma }^{-1}H{)}^{-1}{H}^T{\Sigma }^{-1}x$$