摘要翻译：
我们证明了多重测试过程中错误发现率的控制是由两个耦合的简单充分条件所隐含的。第一个，我们称之为“自洽条件”，与算法本身有关；第二个，称为“依赖控制条件”，与$P$-value族上的依赖假设有关。许多标准的多重测试过程都是自洽的（如逐步上升、逐步下降或逐步上升-下降过程），我们证明了在三种经典的依赖类型：独立、正依赖(PRDS)和未指定依赖中，当选择相应合适的拒绝函数时，依赖控制条件可以满足。因此，我们通过简单和统一的证明恢复了早期的结果，同时将其范围扩展到几个方面：加权FDR、$P$-值重新加权、未指定的$P$-值依赖下的新的升压过程族和自适应升压过程。我们给出了其他可能应用的额外例子。该框架还允许定义和研究在一个连续的、不可数的假设空间上的多个测试过程的FDR控制。
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英文标题：
《Two simple sufficient conditions for FDR control》
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作者：
Gilles Blanchard (FIRST.IDA), Etienne Roquain (LPMA)
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最新提交年份：
2008
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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：
  We show that the control of the false discovery rate (FDR) for a multiple testing procedure is implied by two coupled simple sufficient conditions. The first one, which we call ``self-consistency condition'', concerns the algorithm itself, and the second, called ``dependency control condition'' is related to the dependency assumptions on the $p$-value family. Many standard multiple testing procedures are self-consistent (e.g. step-up, step-down or step-up-down procedures), and we prove that the dependency control condition can be fulfilled when choosing correspondingly appropriate rejection functions, in three classical types of dependency: independence, positive dependency (PRDS) and unspecified dependency. As a consequence, we recover earlier results through simple and unifying proofs while extending their scope to several regards: weighted FDR, $p$-value reweighting, new family of step-up procedures under unspecified $p$-value dependency and adaptive step-up procedures. We give additional examples of other possible applications. This framework also allows for defining and studying FDR control for multiple testing procedures over a continuous, uncountable space of hypotheses.
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PDF链接：
https://arxiv.org/pdf/802.1406