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Math Help - [SOLVED] Sufficiency

  1. #1
    Junior Member
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    [SOLVED] Sufficiency

    Let Y1 and Y2 be two indepent unbiased estimators of . Assume that the variance of Y1 is twice the variance of Y2. Find the constants k1 and k2 so that k1Y1+k2Y2 is an unbiased estimator with smallest possible variance for such a linear combination.
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    So Var I have
    (Y1)=2Var(Y2), E(Y1)=E(Y2)=
    E[(k1Y1+k2Y2)]= --> k1+k2= --> k1+k2=1
    I dont know what to do next.
    Can anyone help?
    Thanks.
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  2. #2
    MHF Contributor matheagle's Avatar
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    V(aX+bY)= a^2V(X)+b^2V(Y)=a^2V(X)+2b^2V(X)=V(X)(a^2+2b^2)

    Then use LaGrange since you want to minimize a^2+2b^2 given a+b=1.
    This seems to be 2/3 and 1/3. I initially thought this would be 1 and 0.
    Last edited by matheagle; April 17th 2009 at 04:18 PM.
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