1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear Estimator - Need Help

  1. Apr 22, 2008 #1
    1. The problem statement, all variables and given/known data
    Given
    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

    has

    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?