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Linear Estimator - Need Help

  • Thread starter purplebird
  • Start date
18
0
1. Homework Statement
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
 

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