# Weights of a linear estimator

1. Apr 22, 2008

### purplebird

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 = $$\sigma(i)$$^2

Find W(i) such that the linear estimator

$$\mu$$ = $$\sum$$W(i)X(i) for i = 1 to N

has

mean value of $$\mu$$= u

and E[(u- $$\mu$$)^2 is a minimum

3. The attempt at a solution

For a linear estimator:

W(i) = R$$^{}-1$$b

where b(i)= E($$\mu$$(i) X(i)) and R(i) = E(X(i)X(j))

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