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

For an estimator $T$ of $\theta$, its bias and mean squared error areWhen the second moment exists, expanding around ${\mathbb{E}}_{\theta }[T]$ gives the bias-variance decomposition ${\mathrm{MSE}}_{\theta }(T)={\mathrm{Var}}_{\theta }(T)+b_{\theta }(T{)}^2$.