= Solution
For <Jackknife resampling>, calculate the leave-one-out estimates $\widehat\theta_{(-i)}$ by deleting observation $i$, and their average $\overline\theta_J=n^{-1}\sum_i\widehat\theta_{(-i)}$. The <Jackknife variance estimator> is
$$
\boxed{\widehat V_J=\frac{n-1}{n}\sum_{i=1}^n(\widehat\theta_{(-i)}-\overline\theta_J)^2.}
$$
The factor $n-1$ compensates for the small differences between the overlapping samples. For sufficiently smooth <statistics> it estimates their <sampling variance>. The related estimated bias is $(n-1)(\overline\theta_J-\widehat\theta)$, leading to the <jackknife bias correction> $n\widehat\theta-(n-1)\overline\theta_J$.
For the nonparametric <bootstrap>, replace the unknown distribution by its <empirical distribution function>
$$
\boxed{\widehat F_n(t)=\frac1n\sum_{i=1}^n\mathbf1\{x_i\leq t\}.}
$$
Independently sample $n$ observations with replacement from the original observations, compute the <estimator> on that <bootstrap sample>, and repeat this for $B$ independently generated <bootstrap samples>. If the resulting values are $\widehat\theta_1^*,\ldots,\widehat\theta_B^*$, estimate the conditional <bootstrap> variance by
$$
\boxed{\widehat V_B=\frac1{B-1}\sum_{b=1}^B(\widehat\theta_b^*-\overline\theta^*)^2.}
$$
Its interpretation as an approximation to the original <sampling variance> relies on the <bootstrap> approximating the sampling law of the <statistic>; increasing $B$ only reduces simulation error and cannot repair a failure of that approximation.
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