TABLE OF CONTENTS In this chapter we introduce the principle of the bootstrap, provide a review of basic resampling techniques, and show how the bootstrap can be used to evaluate the distribution of a parameter estimator. We start with non-parametric and parametric bootstrap resampling techniques, which are essentially designed for independent and identically distributed data, followed by bootstrap methods for dependent data. Then, we discuss bootstrap pivotal statistics, the nested (double) bootstrap, and the method of variance stabilisation. We comment on the limitations of the bootstrap, provide some guidance for the application of bootstrap methods in practical situations, and show an example of bootstrap failure. Finally, we sketch other trends in bootstrap resampling methodology.
Let 
= { X 1, X 2, , X n} be a sample, i.e., a collection of n numbers drawn at random from a completely unspecified distribution F. When we say at random we mean that the X i s are independent and identically distributed (iid) random variables, each having distribution F. Let ? denote an unknown characteristic of F. It could be the mean or variance of F or even the spectral density function discussed earlier. The problem we wish to solve is to find the distribution of 
, an estimator of ?, derived from the sample . This is of great practical importance as we need to infer ? based on . For example, if ? is
