Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 4 / 28J / b / iii / Solution

For each $i$, let ${\hat{\theta }}_{(-i)}$ be the same estimator computed after deleting $X_i$, and put ${\overline{\theta }}_{(-)}=n^{-1}{\sum }_i{\hat{\theta }}_{(-i)}$. The jackknife bias correction isIts bias isso the leading $a/n$ term has been removed and the bias is smaller than that of ${\hat{\theta }}_n$.