Abstract (EN)

Various p -values for a composite null hypothesis have had extensive attention in the Bayesian literature, with some preference shown for two versions designated pppost and pcpred ; and it has been indicated that certain candidate p -values can be upgraded to the preceding prefered p -values by the parametric bootstrap. Also recent likelihood theory gives a factorization of a statistical model into a marginal density for a full dimensional ancillary and a conditional density for the maximum likelihood variable. For any given initial or trial statistic that provides a location for a data point we develop: a special version of the Bayesian pcpred , an ancillary based p -value designated panc , and a bootstrap based p -value designated pbs . Then we show under moderate regularity that these are equivalent to the third order and have uniqueness as a determination of the statistical location of the data point, as of course derived from the initial location measure; we also show that they have a uniform distribution to third order, as based on calculations in the moderate-deviations region. This gives three very different routes to a unique p - value corresponding to the initial trial measure of location and the composite null hypothesis. We thus have great flexibility for the derivation of p -values from a convergence of Bayesian and frequentist points of view. Examples are given to indicate the ease and flexibility of the approach.