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摘要翻译：
在过去的十年里，人们已经做出了一些努力，通过线性升压过程(LSU)来控制错误发现率，当测试统计量依赖时，测试$N$假说。本文研究了在null假设下，当n$趋于无穷大时，测试统计量可交换的一些极端参数配置下的期望错误率(EER)和错误发现率(FDR)。所有结果都是以$p$-values的形式导出的。在一般情况下，我们给出了Simes拒绝曲线与$P$-值的（极限）经验分布函数之间相互关系的一系列结果。研究的主要对象是这些函数之间的最大（极限）交叉点，它们在导出EER和FDR的显式公式中起着关键作用。作为具体的例子，我们对等相关正态和$T$-变量进行了详细的研究，并从理论和数值上计算了极限EER和FDR。如果这些模型趋于独立，就会出现令人惊讶的极限行为。
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英文标题：
《Dependency and false discovery rate: Asymptotics》
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作者：
Helmut Finner, Thorsten Dickhaus, Markus Roters
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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：
Some effort has been undertaken over the last decade to provide conditions for the control of the false discovery rate by the linear step-up procedure (LSU) for testing $n$ hypotheses when test statistics are dependent. In this paper we investigate the expected error rate (EER) and the false discovery rate (FDR) in some extreme parameter configurations when $n$ tends to infinity for test statistics being exchangeable under null hypotheses. All results are derived in terms of $p$-values. In a general setup we present a series of results concerning the interrelation of Simes' rejection curve and the (limiting) empirical distribution function of the $p$-values. Main objects under investigation are largest (limiting) crossing points between these functions, which play a key role in deriving explicit formulas for EER and FDR. As specific examples we investigate equi-correlated normal and $t$-variables in more detail and compute the limiting EER and FDR theoretically and numerically. A surprising limit behavior occurs if these models tend to independence.
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PDF链接：
https://arxiv.org/pdf/710.3171
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