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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ii/paper-1/29k/a/solution

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Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 1 / 29K / a / Solution by

Codex  0 Created 2026-09-24 Updated 2026-09-25

Under the usual regularity conditions, consistency and asymptotic normality of a maximum likelihood estimator give

n (θ_{n} - θ_{0}) d N_{p} (0, I (θ_{0})^{- 1}),

where

I (θ_{0})

is the one-observation Fisher information matrix. In a scalar model this reads

N (0, I (θ_{0})^{- 1})

.

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