平均显著性水平控制检验的错误发现率调整
False Discovery Rate Adjustments for Average Significance Level Controlling Tests
AI总结：
研究在平均显著性水平控制下，Benjamini-Hochberg过程仍能渐近控制FDR，并证明某些依赖调整在有限样本中有效，为高维非参数设置提供FDR控制方法。
摘要：
多重检验调整，例如控制错误发现率（FDR）的Benjamini & Hochberg（1995）逐步上升程序，通常应用于在经典意义上控制显著性水平的检验族：对于每个单独检验，错误拒绝的概率不超过名义水平。在本文中，我们考虑仅满足较弱显著性水平控制概念的检验，其中错误拒绝的概率只需在假设上平均控制。我们发现，Benjamini & Hochberg（1995）逐步上升程序在具有许多弱相关p值和拒绝数量增加的渐近情况下仍然控制FDR，并且对相关p值的某些调整（例如Benjamini & Yekutieli（2001）程序）在有限样本中继续产生FDR控制。我们的结果为在非参数和高维设置中采用FDR控制程序打开了大门，其中弱化推断概念可能允许提高功效。
英文摘要：
Multiple testing adjustments, such as the Benjamini & Hochberg (1995) step-up procedure for controlling the false discovery rate (FDR), are typically applied to families of tests that control significance level in the classical sense: for each individual test, the probability of false rejection is no greater than the nominal level. In this paper, we consider tests that satisfy only a weaker notion of significance level control, in which the probability of false rejection need only be controlled on average over the hypotheses. We find that the Benjamini & Hochberg (1995) step-up procedure still controls FDR in the asymptotic regime with many weakly dependent p-values and an increasing number of rejections, and that certain adjustments for dependent p-values such as the Benjamini & Yekutieli (2001) procedure continue to yield FDR control in finite samples. Our results open the door to FDR controlling procedures in nonparametric and high dimensional settings where weakening the notion of inference may allow for power improvements.
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