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Weights of a linear estimator

  1. Apr 22, 2008 #1
    I know I already posted this but I made a mistake in the original post which I realized now and I am reposting the correct problem as i am not able to edit it.

    1. The problem statement, all variables and given/known data
    X(i) = u + e(i) i = 1,2,...N
    such that e(i)s are statistically independent and u is a parameter
    mean of e(i) = 0
    and variance = [tex]\sigma(i)[/tex]^2

    Find W(i) such that the linear estimator

    [tex]\mu[/tex] = [tex]\sum[/tex]W(i)X(i) for i = 1 to N


    mean value of [tex]\mu[/tex]= u

    and E[(u- [tex]\mu[/tex])^2 is a minimum

    3. The attempt at a solution

    For a linear estimator:

    W(i) = R[tex]^{}-1[/tex]b

    where b(i)= E([tex]\mu[/tex](i) X(i)) and R(i) = E(X(i)X(j))

    I do not know how to proceed beyond this. Thanks for your help
  2. jcsd
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