What is the jackknife?

hard

Answer

$Leave-one-out precursor of the bootstrap.$
$For each i, compute θ̂_(-i) = statistic on data without observation i.$
$({\theta}( - i)\; - \;{\theta})^{2}$
$Bias correction: n * θ̂ - (n-1) * θ̄.$
$Cheaper than bootstrap (n evaluations vs B \approx 1000), but less general — works only for smooth statistics (fails for medians, quantiles).$
$Foundation of influence-function-based robust statistics.$

Check yourself — multiple choice

Same as bootstrap
Leave-one-out SE estimator; cheap (n evals) but only works for smooth statistics (fails on medians / quantiles)
Only Bayesian
Not real

Jackknife: LOO SE estimator; smooth statistics only; bootstrap ancestor.

#bootstrap#estimation

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