When testing many hypotheses, often we do not have strong expectations about the directions of the effects. In some situations however, the alternative hypotheses are that the parameters lie in a certain direction or interval, and it is in fact expected that most hypotheses are false. This is often the case when researchers perform multiple noninferiority or equivalence tests, e.g. when testing food safety with metabolite data. The goal is then to use data to corroborate the expectation that most hypotheses are false. We propose a nonparametric multiple testing approach that is powerful in such situations. If the user's expectations are wrong, our approach will still be valid but have low power. Of course all multiple testing methods become more powerful when appropriate one-sided instead of two-sided tests are used, but our approach often has superior power then. The proposed methods are not at all limited to safety testing and can be used for testing hypotheses about various kinds of parameters, such as coefficients of a model. The methods in this paper control the median of the false discovery proportion (FDP), which is the fraction of false discoveries among the rejected hypotheses. This approach is comparable to false discovery rate control, where one ensures that the mean rather than the median of the FDP is small. Our procedures make use of a symmetry property of the test statistics, do not require independence and have finite-sample properties.

翻译：当检验多个假设时，我们通常对效应的方向没有强烈的预期。然而在某些情况下，备择假设要求参数位于特定方向或区间内，且实际上预期大多数假设均为伪。这在研究者进行多重非劣效性或等效性检验时尤为常见，例如使用代谢物数据检验食品安全性的场景。此时的目标是利用数据证实"大多数假设为伪"这一预期。本文提出了一种在此类情境下具有高效力的非参数多重检验方法。若使用者的预期有误，本方法仍能保持有效性，但效力会降低。当然，当采用适当的单侧检验而非双侧检验时，所有多重检验方法的效力都会提升，而本方法在此条件下往往具有更优的效力。所提出的方法绝不局限于安全性检验，可适用于各类参数的假设检验，例如模型系数。本文方法控制的是错误发现比例的中位数——即在拒绝的假设中错误发现所占的比例。该方法与错误发现率控制具有可比性，后者确保的是FDP的均值（而非中位数）较小。我们的程序利用了检验统计量的对称特性，不要求独立性假设，且具有有限样本性质。