 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2006/ii/paper-1/27j/b/solution

For any rule

d

, the average risk is at most its supremum, and the specified Bayes-optimality property then gives

sup_{θ} R (θ, d) \geq r (π_{0}, d) \geq r (π_{0}, d^{*}) = sup_{θ} R (θ, d^{*}) .

Therefore $d^{*}$ is minimax.

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