Bootstrapping (statistics)

Bootstrapping is in the statistics a method of resampling. This statistics based only calculates a sample repeatedly. Find use bootstrap methods when the theoretical distribution of the statistic of interest is not known. This method was first described by Bradley Efron in 1979, Bootstrap Methods: Another Look at the described jackknife.

The bootstrap generally replaces the theoretical distribution function of a random variable by the empirical distribution function (relative cumulative frequency function) of the sample.

Procedure

For B bootstrap samples are generated by the simplest case, that is ever drawing n times from the given sample, a value drawn with replacement. This corresponds to the repeated drawing of random numbers from the empirical distribution function. For each bootstrap sample, the value of the interesting statistic T is calculated. The distribution of is finally approximated by the empirical distribution of the B values ​​.

In less intuitive models repeatedly drawing from the already existing data is carried out not only. Methodically can be divided into bootstrap method also proceed that certain characteristics of the unknown distribution are estimated and based on this information data is re-generated by a distribution with the estimated sizes is produced. Especially when statistical tests can not be performed because, for example, the exact distribution of the test statistic and the unknown sample is too small for the fulfillment of the convergence criteria, quantiles and p- values ​​can be underestimated.