Results 1 to 2 of 2

Math Help - Smallest variance

  1. #1
    Member
    Joined
    Oct 2008
    Posts
    206

    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 09:17 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Oct 2009
    Posts
    340
    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.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 13
    Last Post: May 12th 2011, 05:32 AM
  2. variance of the sample variance
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: February 8th 2011, 09:35 PM
  3. How to get new variance given old variance and average
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: November 23rd 2010, 06:39 AM
  4. Replies: 2
    Last Post: March 26th 2009, 07:58 PM
  5. Variance of the population variance.
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: November 10th 2008, 10:07 AM

Search Tags


/mathhelpforum @mathhelpforum