Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 4 / 28L / c / Solution

Combining the risk assumption with Cramer-Rao bound gives $(1+b^{\prime }{)}^2\le \gamma -I{b}^2$. Taking the branch compatible with super-efficiency yields $b^{\prime }\le -[1-\sqrt{\gamma -I{b}^2}]\le -(1-\sqrt{\gamma })$, equivalent to the displayed sharper pointwise inequality.