this question relates to the requirement for achieving CRLB.
I know that for a random sample $Y_1, \ldots, Y_n$, an estimator $U$ of $g(\theta)$ is MVUE (i.e. it is unbiased and also $\operatorname{Var}(U) = \frac{[\frac{\delta}{\delta\theta}g(\theta)]^2}{I_Y{(\theta})}$), then it also achieves its CRLB. However if the logic flows the other way, that is to say, for the unbiased estimator $U$, $U$ achieves its CRLB iff $s(\theta;y) = b(\theta)(h(y) - g(\theta))$.
My question:
Can someone please explain, intuitively, this requirement $s(\theta;y) = b(\theta)(h(y) - g(\theta))$ please?
Many thanks