Bootstrapping

Bootstrapping alludes to a German legend about a Baron Münchhausen, who was able to lift himself out of a swamp by pulling himself up by his own hair. In later versions he was using his own boot straps to pull himself out of the sea which gave rise to the term .

Statistics

In statistics bootstrapping is a method for estimating the sampling distribution of an estimator by resampling with replacement from the original sample.

Related Topics:
Statistics - Sampling distribution - Estimator - Resampling

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The bootstrap was invented by Bradley Efron (1979, 1981, 1982) and further developed by Efron and Tibshirani (1993). "Bootstrap" means that resampling one available sample gives rise to many others, reminiscent of pulling yourself up by your bootstraps. While the original objective of cross-validation was to verify replicability of results and that of jackknife is to detect outliers, Efron (1981, 1982) developed bootstrap for inferential purposes.

Related Topics:
Cross-validation - Jackknife - Outlier - Inferential

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

There are more complicated bootstraps for sampling without replacement, two-sample problems, regression, time series, hierarchical sampling, etc.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

• Hesterberg, T. C., D. S. Moore, S. Monaghan, A. Clipson, and R. Epstein (2005): Bootstrap Methods and Permutation Tests, software.
• Simon, J. L. (1997): Resampling: The New Statistics.

Check particle filter for the general theory of Sequential Monte Carlo methods, as well as details on some common implementations.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~