Solution

Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 3 / 28K / b / Solution

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>.

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 Incoming links: Empirical score outer-product information