Invariant $P$-values for model checking

Abstract

$P$-values have been the focus of considerable criticism based on various considerations. Still, the $P$-value represents one of the most commonly used statistical tools. When assessing the suitability of a single hypothesized distribution, it is not clear that there is a better choice for a measure of surprise. This paper is concerned with the definition of appropriate model-based $P$-values for model checking.Comment: Published in at http://dx.doi.org/10.1214/09-AOS727 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org