Testing goodness-of-fit and conditional independence with approximate co-sufficient sampling

Goodness-of-fit (GoF) testing is ubiquitous in statistics, with direct ties to model selection, confidence interval construction, conditional independence testing, and multiple just name a few applications. While the GoF of simple (point) null hypothesis provides an analyst great flexibility choice test statistic while still ensuring validity, most tests for composite hypotheses are far more constrained, as must have tractable distribution over entire space. A notable exception co-sufficient sampling (CSS): resampling data on sufficient guarantees valid using any chooses. But CSS requires compact (in information-theoretic sense) statistic, which only holds very limited class models; even logistic regression, powerless. In this paper, we leverage concept approximate sufficiency generalize essentially parametric asymptotically efficient estimator; call our extension “approximate CSS” (aCSS) testing. We quantify finite-sample Type I error inflation aCSS show that it vanishing under standard maximum likelihood asymptotics, statistic. apply proposed procedure both theoretically simulation number models interest demonstrate its power.