 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ii/paper-2/28k/b/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

An admissible estimator is one for which there is no estimator

δ

satisfying

R (θ, δ) \leq R (θ, θ)

for every

θ

, with strict inequality for at least one

θ

. For

p \geq 3

δ_{JS} (X) = (1 - \frac{p - 2}{∥ X ∥ ^{2}}) X

R (θ, δ_{JS}) = p - (p - 2)^{2} E_{θ} \frac{1}{∥ X ∥ ^{2}} < p .

It strictly dominates

X

, and hence

θ_{MLE} is inadmissible .

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