Among all GLS estimators, Why is the GLS estimator with the true $\displaystyle \sum$ achieves the smallest variance?

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- Apr 16th 2011, 08:04 AMnoob mathematicianSmallest variance
Among all GLS estimators, Why is the GLS estimator with the true $\displaystyle \sum$ achieves the smallest variance?

- Apr 16th 2011, 08:52 AMtheodds
It's a consequence of the Gauss-Markov theorem. You just transform the GLS problem by left-multiplying by \Sigma^{1/2} and then apply Gauss-Markov.