Resampling statistics are methods that construct repeated datasets from an observed sample or a fitted probability model in order to approximate the behavior of a statistic under repeated sampling. They are used to estimate estimator bias and standard error, construct confidence intervals, and approximate null distributions when a convenient analytic sampling distribution is unavailable.
The principal resampling schemes answer different questions. In nonparametric statistics, bootstrap methods sample with replacement from the empirical distribution function, while parametric bootstrap methods simulate from a fitted model. The jackknife systematically deletes observations and recomputes a statistic. A permutation test rearranges observations or labels using transformations that are valid under a specified null hypothesis. For dependent observations, the resampling scheme must preserve the relevant dependence structure.
