Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 1 / 5J / a

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- Solution a

Solution

For log-likelihood

ℓ (β; Y)

, the score function and Fisher information matrix are

U (β) = \nabla_{β} ℓ (β; Y), I (β) = - E_{β} [\nabla_{β}^{2} ℓ (β; Y)] = cov_{β} (U (β)) .

The Fisher scoring iteration replaces the observed Hessian in Newton's method by its expectation:

β^{(m + 1)} = β^{(m)} + I (β^{(m)})^{- 1} U (β^{(m)}) .

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