摘要翻译：
假发现率(FDR)范式的目的是在多重假设检验中以相对较高的功率对I型错误进行一定的控制。Benjamini-Hochberg(BH)程序是一种著名的FDR控制程序。在随机效应模型下，我们表明，与FDR不同，BH过程的正FDR（pFDR）通常不能控制在任意低的水平，因为观察提供的分离假零和真零的证据有限。这导致临界现象，其特征是一旦目标FDR控制水平低于正临界值，程序的功率从正向渐近0过渡，而pFDR没有任何降低。为了解决临界现象对功率和pFDR控制的限制，我们提出了一个在$P$-值域的多个位置应用BH型过程的过程。分析和仿真结果表明，该方法能显著提高功率和pFDR控制性能。
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英文标题：
《On the performance of FDR control: Constraints and a partial solution》
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作者：
Zhiyi Chi
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最新提交年份：
2007
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分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  The False Discovery Rate (FDR) paradigm aims to attain certain control on Type I errors with relatively high power for multiple hypothesis testing. The Benjamini--Hochberg (BH) procedure is a well-known FDR controlling procedure. Under a random effects model, we show that, in general, unlike the FDR, the positive FDR (pFDR) of the BH procedure cannot be controlled at an arbitrarily low level due to the limited evidence provided by the observations to separate false and true nulls. This results in a criticality phenomenon, which is characterized by a transition of the procedure's power from being positive to asymptotically 0 without any reduction in the pFDR, once the target FDR control level is below a positive critical value. To address the constraints on the power and pFDR control imposed by the criticality phenomenon, we propose a procedure which applies BH-type procedures at multiple locations in the domain of $p$-values. Both analysis and simulations show that the proposed procedure can attain substantially improved power and pFDR control.
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PDF链接：
https://arxiv.org/pdf/710.3287