Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 205 / 5 / e

Apply the stated deterministic equivalent for the squared resolvent with ${\Theta }_p={\beta }^0({\beta }^0{)}^T/r^2$. The bias term tends to $-{\ell }^2{r}^2{m}^{\prime }(\ell )$. For the variance useNormalized traces and $p/n\to \gamma$ therefore giveThus the conclusion printed in the paper also has both signs involving $m^{\prime }$ reversed. The hypotheses as printed imply the formula above; they cannot imply the requested one because $(\hat{\Sigma }+\ell I{)}^{-2}$ is positive definite while $m^{\prime }(\ell )\le 0$ for a resolvent limit.