TABLE OF CONTENTS In this chapter, we have introduced the ideas behind the bootstrap principle. We have discussed the non-parametric as well as the parametric bootstrap. The exposure of the bootstrap has been supported with numerous examples for both iid as well as dependent data. We have covered bootstrap methods for dependent data, such as the moving block bootstrap, but we have also shown, by way of example, how one can use the independent data bootstrap to tackle complicated data structures such as autoregressions. The examples presented in this chapter demonstrate the power of the bootstrap and its superior performance compared to classical methods based, for example, on asymptotic theory. This being said, care is required when applying the bootstrap. Thus, we reported a case where the bootstrap fails.
The reader should note the following points, which we have emphasised throughout the chapter.
The parametric bootstrap outperforms the non-parametric bootstrap when the number of samples is small. However, this holds only if the assumed model is correct. Generally speaking, the non-parametric bootstrap is more robust than the parametric bootstrap.
It is relatively easy to use the bootstrap in linear models if the errors are iid. This, however, may not be given in practice. The approach would be to use a dependent data resampling scheme, such as the moving block bootstrap. This, however, requires large sample sizes (say n > 1000). It is often worth the effort to attempt to linearise the problem and use the concept of residuals.
