Empirical score outer-product information
= Empirical score outer-product information
The empirical score outer-product matrix is
$$
i_n(\theta)=\frac1n\sum_{j=1}^n
\nabla_\theta\log f(X_j,\theta)
\nabla_\theta\log f(X_j,\theta)^T.
$$
Under regularity and consistency of $\widehat\theta$, $i_n(\widehat\theta)$ converges in probability to the <Fisher information matrix>. This convention differs from the negative-Hessian convention for <Observed Fisher information>.