Jackknife resampling

In statistics, the jackknife is a resampling technique especially useful for variance and bias estimation. The jackknife predates other common resampling methods such as the bootstrap. The jackknife estimator of a parameter is found by systematically leaving out each observation from a dataset and calculating the estimate and then finding the average of these calculations. Given a sample of size ${\displaystyle N}$, the jackknife estimate is found by aggregating the estimates of each ${\displaystyle N-1}$-sized sub-sample.

The jackknife technique was developed by Maurice Quenouille (1949, 1956). John Tukey (1958) expanded on the technique and proposed the name "jackknife" since, like a physical (a compact folding knife), it is a tool that can improvise a solution for a variety of problems even though specific problems may be more efficiently solved with a purpose-designed tool.

The jackknife is a linear approximation of the bootstrap.

The jackknife estimate of a parameter can be found by estimating the parameter for each subsample omitting the ith observation to estimate the previously unknown value of a parameter (say ${\displaystyle {\bar {x}}_{i}}$).

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