4.4 Bootstrap

Bootstrap was proposed by Efron [39] as a computer-based technique to estimate the accuracy of a generic estimator $\hat{\boldsymbol {\theta }}$.

Bootstrap relies on a data-based simulation method for statistical inference. The use of the term bootstrap derives from the phrase to pull oneself up by one’s bootstrap, widely thought to be based on one of the eighteenth century Adventures of Baron Munchausen, by R.E. Raspe. The Baron had fallen to the bottom of a deep lake. Just when it looked like all was lost, he thought to pick himself up by his own bootstraps 1.

The idea of bootstrap is very simple, namely that in absence of any other information, the sample itself offers the best guide of the sampling distribution. The method is completely automatic, requires no theoretical calculation, and is available no matter how mathematically complicated the estimator $\hat{\boldsymbol {\theta }}$ is. By resampling with replacement from $D_ N$ we can build a set of $B$ datasets $D_{(b)}, b=1,\dots ,B$. From the empirical distribution of the statistics $t(D_{(b)})$ we can construct confidence intervals and tests for significance.

  1. This term has not the same meaning (though the derivation is similar) as the one used in computer operating systems where bootstrap stands for starting a computer from a set of core instructions