Introduction

In previous chapters our models have involved variables independent at some level, and we have been able to identify independent components that can be simulated. Where a model can be fitted and residuals of some sort identified, the same ideas can be applied in the more complex problems discussed in this chapter. Where that model is parametric, parametric simulation can in principle be used to obtain resamples, though Markov chain Monte Carlo techniques may be needed in practice. But in nonparametric situations the dependence may be so complex, or our knowledge of it so limited, that neither of these approaches is feasible. Of course some assumption of repeatedness within the data is essential, or it is impossible to proceed. But the repeatability may not be at the level of individual observations, but of groups of them, and there is typically dependence between as well as within groups. This leads to the idea of constructing bootstrap data by taking blocks of some sort from the original observations. The area is in rapid development, so we avoid a detailed mathematical exposition, and merely sketch key aspects of the main ideas. In Section 8.2 we describe some of the resampling schemes proposed for time series. Section 8.3 outlines some ideas useful in resampling point processes.