Evento rientra nelle attività organizzate per il 40° Anniversario di Economia

Abstract: Confidence distributions provide a fully frequentist framework for representing uncertainty about a parameter as a distribution, from which point estimates, p-values, and confidence intervals at any level can be extracted. An exact confidence distribution is one whose confidence intervals achieve nominal coverage at every confidence level. In practice, exactness is difficult to achieve for instance when combining information across multiple probability models with multiple parameters with nuisance components. Existing approaches commonly uses Wilks' theorem to profile likelihood ratio statistics, which is broadly applicable but relies on large-sample approximations and regularity conditions that might be broken; in particular, parameters under the null hypotheses must lie in the interior of the parameter space. In this talk, we discuss our ongoing work on corrections to these methods when parameters are bounded. Additionally, we present our Exact Confidence Curve Combination method, a new approach for combining information that requires neither asymptotic approximations nor interiority conditions and can accommodate multidimensional parameters perhaps also with nuisance components. We demonstrate both contributions in a common high-energy physics application: the Poisson signal-plus-background experiment.