Solution
= Solution
For each $i$, let $\widehat\theta_{(-i)}$ be the same estimator computed after deleting $X_i$, and put $\overline\theta_{(-)}=n^{-1}\sum_i\widehat\theta_{(-i)}$. The <jackknife bias correction> is
$$
\boxed{\widehat\theta_{\mathrm J}
=n\widehat\theta_n-(n-1)\overline\theta_{(-)}.}
$$
Its bias is
$$
nB_n(\theta_0)-(n-1)B_{n-1}(\theta_0)=O(n^{-2}),
$$
so the leading $a/n$ term has been removed and the bias is smaller than that of $\widehat\theta_n$.