Functional delta method
= Functional delta method
{title2=$r_n(\Phi(X_n)-\Phi(s))\xrightarrow d\dot\Phi_s(X)$}
If $r_n(X_n-s)$ converges in distribution to $X$ and $\Phi$ is <Hadamard differentiable> at $s$ tangentially to a space containing the limit, the displayed transformation rule holds under the usual <measurability> and tight separable-support conditions. The variables $X_n$ must belong to the domain of $\Phi$.