Demystifying bootstrapping

The most well-known resampling technique is the one defined as bootstrapping, as introduced by B. Efron in 1993. The logic of the bootstrap method is to build samples that are not observed, but statistically like those observed. This is achieved by resampling the observed series through an extraction procedure where we reinsert the observations.

Introducing bootstrapping

This procedure is like extracting a number from an urn, with subsequent reinsertion of the number before the next extraction. Once a statistical test has been chosen, it is calculated both on the observed sample and on a large number of samples of the same size as that observed and obtained by resampling. The N values of the test statistic then allow us to define the sample distribution; that is, the empirical distribution of the chosen statistic.

Important Note

A statistical test is a rule for discriminating samples that, if observed, lead to the rejection of an initial hypothesis...