Bootstrapping (statistics)
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In statistics, bootstrapping is a method for assigning measures of accuracy (defined in terms of bias, variance, confidence intervals, prediction error or some other such measure) to sample estimates.[1][2] This technique allows estimation of the sampling distribution of almost any statistic using only very simple methods.[3][4] Generally, it falls in the broader class of resampling methods.
Bootstrapping is the practice of estimating properties of an estimator (such as its variance) by measuring those properties when sampling from an approximating distribution. One standard choice for an approximating distribution is the empirical distribution of the observed data. In the case where a set of observations can be assumed to be from an independent and identically distributed population, this can be implemented by constructing a number of resamples of the observed dataset (and of equal size to the observed dataset), each of which is obtained by random sampling with replacement from the original dataset.
It may also be used for constructing hypothesis tests. It is often used as an 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.
Contents
* 1 History * 2 Approach * 3 Situations where bootstrapping is useful * 4 Discussion * 4.1 Advantages * 4.2 Disadvantages * 4.3 Recommendations * 5 Types of bootstrap scheme * 5.1 Case resampling * 5.1.1 Estimating the distribution of sample mean * 5.1.2 Regression * 5.2 Bayesian bootstrap * 5.3 Smooth bootstrap * 5.4 Parametric bootstrap * 5.5 Resampling residuals * 5.6 Gaussian process regression bootstrap * 5.7