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摘要翻译：
在假设检验中，多元统计通常是可用的，也是必要的。我们研究了如何利用这种统计量来控制假发现率(FDR)，并以良好的功率控制正FDR（pFDR）。我们证明了FDR可以通过检验统计量的多元$P$-值的嵌套区域来控制。如果测试统计量的分布已知，则可以显式地构造区域，在满足一定条件的过程中实现最大功率的FDR控制。另一方面，我们的重点是那些只知道部分分布的地方。在一定的条件下，提出了一类嵌套区域，并证明了当pFDR控制水平接近其可达极限时，该区域能达到渐近最大功率的(p)FDR控制。将基于嵌套区域的过程与基于其他更容易构造的嵌套区域的过程以及基于更直接的测试统计量组合的过程进行了比较。
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英文标题：
《False discovery rate control with multivariate $p$-values》
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作者：
Zhiyi Chi
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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：
Multivariate statistics are often available as well as necessary in hypothesis tests. We study how to use such statistics to control not only false discovery rate (FDR) but also positive FDR (pFDR) with good power. We show that FDR can be controlled through nested regions of multivariate $p$-values of test statistics. If the distributions of the test statistics are known, then the regions can be constructed explicitly to achieve FDR control with maximum power among procedures satisfying certain conditions. On the other hand, our focus is where the distributions are only partially known. Under certain conditions, a type of nested regions are proposed and shown to attain (p)FDR control with asymptotically maximum power as the pFDR control level approaches its attainable limit. The procedure based on the nested regions is compared with those based on other nested regions that are easier to construct as well as those based on more straightforward combinations of the test statistics.
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PDF链接：
https://arxiv.org/pdf/706.0498
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