Some point estimator, mu hat, is given by the following:
mu hat = .2X1 + 2.5X2 - X3 - .7X4
There are 4 samples (Xi). I am asked to determine whether this mu hat is a BLUE estimator of mu.
I can prove that mu hat is unbiased by taking the expected value of the expression, and I can show that mu hat is not a linear estimator. Since it is not even a linear estimator, I would expect that this is not a BLUE estimator. But I feel like I get in trouble when I make assumptions, so I thought I'd ask if somebody could shed some light here. Thanks.