Definition: Let $X_i \iid p(x \vert \bt^\ast)$. Suppose a sequence of estimates $\bth_n$ for $\bt$ satisfies
\[\sqrt{n}(\bth_n-\bt) \inD \Norm(\zero, \bS(\bt)).\]The sequence is said to be asymptotically efficient if $\bS(\bt) = \fI^{-1}(\bt)$ for all $\bt$.
Note: it is common usage in statistics to refer to such estimators as simply “efficient”, although “asymptotically efficient” is a more accurate term.