Resampling methods approximate the sampling distribution of a statistic or estimator. In essence, a sample taken from the population is treated as a population itself. A large number of new samples, or resamples, are taken from this “new population”, commonly with replacement, and within each of these resamples, the estimate of interest is re-obtained. A large number of these estimate replicates can then be used to construct the empirical sampling distribution from which confidence intervals, bias, and variance may be estimated. These methods are particularly advantageous for statistics or estimators for which no standard methods apply or are difficult to derive.
The jackknife is a popular resampling method, first introduced by Quenouille in 1949 as a method of bias estimation. In 1958, jackknifing was both named by Tukey and expanded to include variance estimation. A jackknife is a multipurpose tool, similar to a swiss army knife, that can get its user out of tricky situations. Efron later developed the arguably most popular resampling method, the bootstrap, in 1979 after being inspired by the jackknife.
In Efron’s (1982) book The jackknife, the bootstrap, and other resampling plans, he states,
Good simple ideas, of which the jackknife is a prime example, are our most precious intellectual commodity, so there is no need to apologize for the easy mathematical level.
Despite existing since the 1940’s, resampling methods were infeasible due to the computational power required to perform resampling and recalculate estimates many times. With today’s computing power, the uncomplicated yet powerful jackknife, and resampling methods more generally, should be a tool in every analyst’s toolbox.
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