Bootstrap confidence bands and goodness-of-fit tests in simulation input/output modelling

In the analysis of input and output models used in computer simulation, parametric bootstrapping provides an attractive alternative to asymptotic theory for constructing confidence intervals for unknown parameter values and functions involving such parameter values, and also for calculating critical values of EDF statistics used in goodness-of-fit tests, such as the Anderson-Darling A² statistic. This latter is known to give a GoF test that clearly out-performs better known tests such as the chi-squared test, but is hampered by having a null distribution that varies with different null hypotheses including whether parameters are estimated or not. Parametric bootstrapping offers an easy way round the difficulty, so that the A² test can routinely be applied. Moreover we show that bootstrapping is probabilistically exact for location-scale models, and so in general will be reasonably accurate using a mean and standard deviation parametrization. A numerical example is given.