Bootstrap and Permutation Methods
The impact of the bootstrap has transcended both theory and applications. The bootstrap has shown us how to use the power of the computer and iterated calculations to go where theoretical calculations cannot, which introduces a different way of thinking about all of statistics. Bootstrap methods and other computationally intensive methods of statistical estimation and inference have a long history dating back to the permutation test introduced in the 1930s by R. A. Fisher. The most common use of the bootstrap method is to approximate the sampling distribution of a statistic, such as the mean, median, regression slope, or correlation coefficient. Once the sampling distribution has been approximated via the bootstrap method, estimation and inference involving the given statistic follow in a straightforward manner. The ease of calculation of various sample quantities for a given statistic is the reason why the bootstrap method was so popular when Efron first developed it.