Exact confidence intervals generated by conditional parametric bootstrapping

Conditional parametric bootstrapping is defined as the samples obtained by performing the simulations in such a way that the estimator is kept constant and equal to the estimate obtained from the data. Order statistics of the bootstrap replicates of the parameter chosen in each simulation provide exact confidence intervals, in a probabilistic sense, in models with one parameter under quite general conditions. The method is still exact in the case of nuisance parameters when these are location and scale parameters, and the bootstrapping is based on keeping the maximum-likelihood estimates constant. The method is also exact if there exists a sufficient statistic for the nuisance parameters and if the simulations are performed conditioning on this statistic. The technique may also be used to construct prediction intervals. These are generally not exact, but are likely to be good approximations.