We derive inferential procedures for large sample sizes that remain valid under data-dependent significance levels (so-called "post-hoc valid inference"). Classical statistical tools require that the significance level -- the "type-I error" -- is selected prior to seeing or analyzing any data. This restriction leads to some drawbacks. For instance, if an analyst generates an inconclusive confidence interval, repeating the process with a larger significance level is not an option -- the result is final. Recently, e-values have emerged as the solution to this problem, being both necessary and sufficient tools for performing various forms of post-hoc inference. All such results, however, have thus far been nonasymptotic. As a result, they inherit familiar limitations of nonasymptotic inferential procedures such as requiring strong moment assumptions and being conservative in general. This paper develops a theory of post-hoc inference in the asymptotic setting, yielding asymptotic post-hoc confidence sets and asymptotic post-hoc p-values that make weaker assumptions and are sharper than their nonasymptotic counterparts.

翻译：我们推导了适用于大样本的推断方法，这些方法在数据依赖的显著性水平（即所谓的“后验有效推断”）下仍然有效。经典统计工具要求显著性水平——即“第一类错误”——必须在查看或分析任何数据之前预先选定。这一限制导致了一些缺陷。例如，如果分析者生成了一个非结论性的置信区间，则无法通过增大显著性水平来重复该过程——结果即为最终结论。最近，e值作为解决这一问题的工具应运而生，成为执行各种形式后验推断的充分必要条件。然而，迄今为止所有这类结果都是非渐近的。因此，它们继承了非渐近推断方法常见的局限性，例如需要较强的矩假设条件，且通常较为保守。本文发展了渐近框架下的后验推断理论，提出了渐近后验置信集与渐近后验p值，这些方法比非渐近对应方法具有更弱的假设条件且精度更高。