https://doi.org/10.1351/goldbook.10086
Estimation of parameters by multiple re-sampling from measured data to approximate its distribution.
Notes:
- Multiple resamples of the original data allow calculation of the distribution of a parameter of interest, and therefore its standard error (see example).
- Random sampling with replacement is used when the data are assumed to be from an independent and identically-distributed population.
- Bootstrapping is an alternative to cross validation in model validation.
Example: The standard error of an estimate of parameter \(\theta\) \[\hat{s}_{E} = \frac{1}{B} \sum \limits_{i\,=\,1}^{B} (\theta_{i}^{\ast} - \bar \theta^{*})^{2}\] where \(B\) is the number of bootstrap samples, \(\theta_{i}^{\ast}\) the i-th bootstrap estimate, and \({\bar \theta}^{*}\) the mean value of the bootstrap estimates.