Past exam of the mathematics course of the University of Oxford / 2023 / Prelims / Mathematics III / 7 / b / ii / Solution

The inverse moments in part i giveThus the bias is positive, and direct expansion of the mean squared error yieldsFor comparison, the variance is $n^2{\theta }^2/[(n-1{)}^2(n-2)]$; adding the squared bias gives the same answer by the bias-variance decomposition.