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Thread: Smallest variance

  1. April 16th 2011, 08:04 AM #1
    noob mathematician
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    Smallest variance

    Among all GLS estimators, Why is the GLS estimator with the true \sum achieves the smallest variance?
    Last edited by noob mathematician; April 16th 2011 at 08:17 AM.
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  2. April 16th 2011, 08:52 AM #2
    theodds
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    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.
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