Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 3 / 5J / a

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- Solution a

Solution

Writing the log-likelihood as

ℓ (β) = lo g L (β)

, the Fisher information matrix is the expected negative Hessian matrix

I (β) = - E_{β} [\nabla_{β}^{2} ℓ (β)] .

Under the usual regularity conditions it is equivalently the expected outer product of the score function.

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