Resampling (statistics)

In statistics, resampling is any of a variety of methods for doing one of the following:

Common resampling techniques include bootstrapping, jackknifing and permutation tests.

Bootstrapping is a statistical method for estimating the sampling distribution of an estimator by sampling with replacement from the original sample, most often with the purpose of deriving robust estimates of standard errors and confidence intervals of a population parameter like a mean, median, proportion, odds ratio, correlation coefficient or regression coefficient. It may also be used for constructing hypothesis tests. It is often used as a robust alternative to inference based on parametric assumptions when those assumptions are in doubt, or where parametric inference is impossible or requires very complicated formulas for the calculation of standard errors. Bootstrapping techniques are also used in the updating-selection transitions of particle filters, genetic type algorithms and related Resample/Reconfiguration Monte Carlo methods used in computational physics and molecular chemistry. In this context, the bootstrap is used to replace sequentially empirical weighted probability measures by empirical measures. The bootstrap allows to replace the samples with low weights by copies of the samples with high weights.

Jackknifing, which is similar to bootstrapping, is used in statistical inference to estimate the bias and standard error (variance) of a statistic, when a random sample of observations is used to calculate it. Historically this method preceded the invention of the bootstrap with Quenouille inventing this method in 1949 and Tukey extending it in 1958. This method was foreshadowed by Mahalanobis who in 1946 suggested repeated estimates of the statistic of interest with half the sample chosen at random. He coined the name 'interpenetrating samples' for this method.

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