Most people who have heard of bootstrapping have only heard of the so-called nonparametric or resampling bootstrap. There are three forms of bootstrapping which differ primarily in how the population is estimated. If T is a cluster dendrogram, we can estimate features such as the proportion of trees in the sampling distribution than include a particular node. For example, if T is quantitative, we are interested in features such as the mean, variance, skewness, etc and also confidence intervals for the mean of T. From this estimated sampling distribution we can estimate the desired features of the sampling distribution. We then (3) take samples 'in silico' (on the computer) from the estimated population, compute T from each (4) and accumulate all of the values of T into an estimate of the sampling distribution. However, taking new samples is expensive, so instead, we take a single sample (1) and use it to estimate the population (2). The true sampling distribution is computed by taking new samples from the true population, computing T and then accumulating all of the values of T into the sampling distribution. The objective is to estimate the true sampling distribution of some quantity T, which may be numeric (such as a regression coefficient) or more complicated (such as a feature cluster dendrogram). Observed quantities are denoted by solid curves and unobserved quantities by dashed curves. The steps in bootstrapping are illustrated in the figure above.

Then samples can be drawn from the estimated population and the sampling distribution of any type of estimator can itself be estimated. The idea is to use the observed sample to estimate the population distribution. Bootstrapping is a method of sample reuse that is much more general than cross-validation.

Xlstat free bootstrapping