Compared to p-values, e-values provably guarantee safe, valid inference. If the goal is to test multiple hypotheses simultaneously, one can construct e-values for each individual test and then use the recently developed e-BH procedure to properly correct for multiplicity. Standard e-value constructions, however, require distributional assumptions that may not be justifiable. This paper demonstrates that the generalized universal inference framework can be used along with the e-BH procedure to control frequentist error rates in multiple testing when the quantities of interest are minimizers of risk functions, thereby avoiding the need for distributional assumptions. We demonstrate the validity and power of this approach via a simulation study, testing the significance of a predictor in quantile regression.

翻译：与p值相比，e值可证明地保证安全、有效的推断。若需同时检验多个假设，可为每个独立检验构造e值，再运用近期发展的e-BH程序对多重性进行适当校正。然而，标准e值构造方法需要可能无法被合理化的分布假设。本文证明，当目标量为风险函数的最小化器时，广义通用推断框架可与e-BH程序结合使用，以控制多重检验中的频率主义错误率，从而避免分布假设的需求。我们通过模拟研究验证了该方法的有效性与功效性，以分位数回归中预测变量显著性检验为例进行演示。