Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 2 / 29K / c / Solution

Put ${\theta }_0=-b/(a-1)$ and compare with the constant estimator
$\delta ={\theta }_0$. Its risk is $(\theta -{\theta }_0{)}^2$. For $a<0$,for every $\theta$, since $|a-1|>1$. Hence the original estimator is inadmissible.

Solved by gpt-5.6-sol high.