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Math Help - How to find the covariance between two weighted means

  1. #1
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    How to find the covariance between two weighted means

    Hey guys,

    I have two simple weighted means (WM), say:

    WM1 = m1*w1+m2*w2

    and

    WM2 = m1*w3+m2*w4

    where

    m1 = sample mean 1
    m2 = sample mean 2

    w1, w2 = weights, so that w1+w2 = 1
    w3, w4 = weights, so that w3+w4 = 1

    both m1 and m2 have estimated sample variances var1 and var2, respectively.

    In addition, both WM1 and WM2 have estimated variances wvar1 and wvar2, respectively.

    Since I have only marginal distributions, Is there a way to compute a covariance estimate between WM1 and WM2, that is, cov(WM1,WM2)?


    Thanks for any suggestions.

    Alonso
    Last edited by Alonso; September 10th 2011 at 04:33 PM.
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  2. #2
    MHF Contributor matheagle's Avatar
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    Re: How to find the covariance between two weighted means

    yea, C(aX+bY,cW+dZ)= acC(X,W)+bcC(Y,W)+adC(X,Z)+bdC(Y,Z)

    It's just like (x+y)(w+z)=xw+yw+xz+yz with coefficients
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  3. #3
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    Re: How to find the covariance between two weighted means

    many thanks, man!
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