Bootstrap methods in computer simulation experiments

We critically review the work that has been done in applying basic, smoothed and parametric bootstrap methods to simulation experiments. We develop a framework to classify bootstrap methods in this context and use it to compare various bootstrap schemes. Most bootstrap methods are hard to analyse theoretically. An exception is the parametric case for which a detailed analysis can be carried out. An interesting result in this case is that, whereas in standard statistical experiments bootstrap samples give only information about the variance of a statistic and not its mean, this turns out not to be so in simulation experiments. Thus parametric bootstrap samples can be advantageously included in estimates of the responses of interest.