Resampling Methods: Randomization Tests, Jackknife and Bootstrap Estimators

Resampling methods are becoming increasingly popular as statistical tools, as they are (generally) very robust, their simplicity is compelling, and their computational demands are (largely) no longer an issue to their widespread implementation. These methods involve either sampling or scrambling the original data numerous times, and we consider three general approaches here. Randomization tests involve taking the original data and either scrambling the order or the association of the original data. Jackknife estimates involve computing the statistic of interest for all combinations of the data where one (or more) of the original data points are removed. Bootstrap approaches attempt to estimate the sampling distribution of a population by generating new samples by drawing (with replacement) from the original data. Our treatment here largely follows the excellent text by Manly (1997). More advanced treatments can be found by Miller (1974), Efron and Gong (1983), Hinkley (1983), Hinkley (1988), Efron and Tibshirani (1986), Good (1994), and Edgington (1995).