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

If $a>1$, compare withIts bias is the negative of the original bias, so the squared-bias terms agree, whileIts risk is therefore strictly smaller for every $\theta$. Thus
${\hat{\theta }}_{a,b}$ is not an admissible estimator.

Solved by gpt-5.6-sol high.