Functional delta method ($r_n(\Phi (X_n)-\Phi (s))\stackrel{d}{\to }{\dot{\Phi }}_s(X)$)

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 $\Phi$.