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Expectation of Covariance Estimate

  1. Feb 24, 2013 #1
    So I'm trying to take the expectation of the covariance estimate.

    I'm stuck at this point. I know I have to separate the instances where i=j for the terms of the form E[XiYj], but I'm not quite sure how to in this instance.

    aCKfxC4.gif

    The answer at the end should be biased, and I'm trying to find a way to make it unbiased. But first tings first, I have to simplify the above.
     
  2. jcsd
  3. Feb 24, 2013 #2
    Is this the next step? What's after that if so?

    3d0pKYL.gif
     
  4. Feb 25, 2013 #3

    chiro

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    Science Advisor

    Hey brojesus111 and welcome to the forums.

    I think you will have to incorporate the mean terms by putting something like + X_bar - X_bar.

    Also given your expression, another that comes to find is try and complete the square in the way of getting E[(X-X_bar)(Y-Y_bar)] by matching this expression with the one you have been given.

    The difference between the two will give the bias.
     
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