Resampling (statistics)

In statistics, resampling is the creation of new samples based on one observed sample. Resampling methods are: Permutation tests (also re-randomization tests) Bootstrapping Cross validation Permutation test Permutation tests rely on resampling the original data assuming the null hypothesis. Based on the resampled data it can be concluded how likely the original data is to occur under the null hypothesis. Bootstrap (statistics) 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 has been called the plug-in principle, as it is the method of estimation of functionals of a population distribution by evaluating the same functionals at the empirical distribution based on a sample. For example, when estimating the population mean, this method uses the sample mean; to estimate the population median, it uses the sample median; to estimate the population regression line, it uses the sample regression line. 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. 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. Cross-validation (statistics) Cross-validation is a statistical method for validating a predictive model.