8 - Resampling Methods

Summary

In the real world, departures from parametric statistical models frequently occur, including mixtures of distributions, outliers and noncentrality. This has led to the development of estimators that are based on resampling of the available data. The most widely used of these is the bootstrap that is based on resampling with replacement from a data set, and may be used to characterize parameter and their bias, along with confidence intervals on them, and testing hypotheses about them. A Monte Carlo approach to remove biass on the Kolmogorov-Smirnov statistic when the distribution parameters are estimated from the data is elucidated. Exact permutation tests based on sampling without replacement from a given data set are defined, and their high power is established. Implementations for one and two sample tests for a location parameter, a two sample test for paired data and a two sample test for dispersion are given. Finally, the jackknife that is a linear approximation to the bootstrap is covered, and is useful for computing estimator variance for very large data sets.