= Solution
Under the standard differentiability, identifiability, moment, and nonsingularity assumptions,
$$
\boxed{
\sqrt n(\widehat\theta-\theta_0)
\xrightarrow{d}N(0,I(\theta_0)^{-1}).}
$$
Here the one-observation score is
$$
S_\theta(X)=\frac{\partial}{\partial\theta}\log f(X,\theta),
$$
and the <Fisher information matrix> is
$$
\boxed{I(\theta)=\mathbb E_\theta[S_\theta(X)S_\theta(X)^T]
=-\mathbb E_\theta\left[\frac{\partial^2}{\partial\theta\partial\theta^T}log f(X,\theta)\right].}
$$
Back to article page
