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Math Help - Weighted least squared error derivation

  1. #1
    Junior Member
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    Weighted least squared error derivation

    I know that the weighted least squares solution is

    B = (X'WX)^-1 . (X'WY)


    Where B is the parameters, X the input, Y the targets and W the weight matrix such that Wii = 1/SD, which in this last case, if I understand it, is optimal if the errors are uncorrelated.

    But does anyone know how to achieve this derivation in matrix notation from the form

    argmin SSE(B) = (Y-XB)'W(Y-XB)?

    Many thanks in advance for any insights.
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  2. #2
    opt
    opt is offline
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    Hi,
    Can you give dimension notation for your matrices/vectors? Usually X and Y have some common dimension and in this formulation it looks like they don't agree.
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