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The bootstrap P-value is the exact tail probability of a test statistic, calculated assuming the nuisance parameter equals the null maximum likelihood (ML) estimate. For discrete data, bootstrap P-values perform amazingly well even for small samples, even as standard first order methods perform surprisingly poorly. Why is this? Detailed numerical calculations in Lloyd (2012a) strongly suggest that the good performance of bootstrap is not explained by asymptotics. In this paper, I establish several desirable non-asymptotic properties of bootstrap P-values. The most important of these is that bootstrap will correct ‘bad’ ordering of the sample space which leads to a more pivotal distribution. Most of the arguments only hold for discrete models and when the null ML estimate is used. Some

Some non-asymptotic properties of parametric bootstrap P-values in discrete models