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Estimated P-Values In Discrete Models: Asymptotic And Non-Asymptotic Effects, Chris Lloyd

Chris J. Lloyd

The exact null distribution of a P-value typically depends on nuisance parameters unspecified under the null. For discrete models and standard approximate P-values, this dependence can be quite strong. The estimated (or bootstrap) P-value is the exact probability of the P-value being no larger than its observed value, with the null estimate of the nuisance parameter substituted. For continuous models, it is known that such `bootstrap' P-values deviate from uniformity by terms of order m^{-3/2}, where m is a measure of sample size. The main difficulty with discrete models is the breakdown of asymptotics near the boundary. The aim of …