MSE Proof for an estimator I am trying to figure out the following proof.
The third line is not clear. We all know that (a+b)^2=a^2+2ab+b^2. The term 2ab should be 0, but I can't figure out why.
I have found other proofs here on this site, but this won't leave me alone, I need to know why 2ab in this case is 0.
Thank you !


$E[T(X)-E(T(X))]=E(T(X))-E(T(X))=0$. (Some of your E have a $\theta$ index and some don't, but actually all of these assume $\theta$, so you can put it everywhere or leave it out everywhere.)
