Introduction

Throughout this book, we have used Monte Carlo simulations to demonstrate statistical properties of estimators. We have simulated data generation processes on the computer and then directly examined the results.

This chapter explains how computer-intensive simulation techniques can be applied to a single sample to estimate a statistic's sampling distribution. These increasingly popular procedures are known as bootstrap methods. They can be used to corroborate results based on standard theory or provide answers when conventional methods are known to fail.

When you “pull yourself up by your bootstraps,” you succeed – on your own – despite limited resources. This idiom is derived from The Surprising Adventures of Baron Munchausen by Rudolph Erich Raspe. The baron tells a series of tall tales about his travels, including various impossible feats and daring escapes. Bradley Efron chose “the bootstrap” to describe a particular resampling scheme he was working on because “the use of the term bootstrap derives from the phrase to pull oneself up by one's own bootstrap … (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.)” [Efron and Tibshirani (1993), p. 5].