$\sqrt{n}(\hat{\theta} - \theta) \xrightarrow{d} N(0, V)$ where $V = A^{-1} B A^{-1}$ with $A = E[\psi'(\theta)]$ and $B = E[\psi(\theta)^2]$.

$\sqrt{n}(\hat{\theta} - \theta) \xrightarrow{d} N(0, 1)$.

The estimator is not asymptotically normal.

The distribution depends only on $A$.