In estimation problems, we may use Cramer-Rao Lower Bound (CRLB) to evaluate the best performance. But if there is no unbiased estimator can attain CRLB, what is the meaning of CRLB?
To clarify the question, I present a simple question here:
$\alpha$ is selected as the evaluating indicator of system $A$. We can obtain the CRLB of $\alpha$, but there is no estimation $\hat \alpha$ which can reach CRLB. Is it reasonable to use the CRLB of $\alpha$ to evaluate the performance of system $A$.