论文标题
错误的发现率调整平均显着性水平控制测试
False Discovery Rate Adjustments for Average Significance Level Controlling Tests
论文作者
论文摘要
多次测试调整，例如Benjamini和Hochberg（1995）控制虚假发现率（FDR）的升级程序，通常应用于在经典意义上控制显着性水平的测试家族：对于每个单独的测试，对于每个单独的测试，假拒绝的可能性不超过名称水平。在本文中，我们考虑仅满足显着性水平控制概念较弱的测试，其中仅需要在假设中平均控制错误拒绝的概率。我们发现Benjamini和Hochberg（1995）的加速程序仍然控制着渐近状态中的FDR，其中许多弱依赖的$ p $值，并且对依赖的$ p $值的某些调整（例如Benjamini和Yekutieli和Yekutieli（2001）的程序（2001年）的程序在有限的样品中继续产生FDR Control。我们的结果为非参数和高维度设置中的FDR控制程序打开了大门，其中削弱了推理概念可以进行大规模的功率改进。
Multiple testing adjustments, such as the Benjamini and 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 and Hochberg (1995) step-up procedure still controls FDR in the asymptotic regime with many weakly dependent $p$-values, and that certain adjustments for dependent $p$-values such as the Benjamini and 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 allows for large power improvements.
