FURTHER RESULTS ON CONTROLLING THE FALSE DISCOVERY PROPORTION
FURTHER RESULTS ON CONTROLLING THE FALSE DISCOVERY PROPORTION
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DOI：
10.1214/14-aos1214
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发表时间：
2014-06-01
影响因子：
4.5
通讯作者：
Sarkar, Sanat K.
中科院分区：
文献类型：
--
作者：
Guo, Wenge;He, Li;Sarkar, Sanat K.
错误发现比例（FDP）超过 gamma 的概率是 [0, 1) 的一个元素，定义为 gamma-FDP，作为多次测试中错误发现的度量而受到广泛关注。尽管该测度因其相关性而被接受，但在非渐近环境下的相关性下推进其理论尚未取得太大进展，这激发了我们在本文中的研究。我们提供了一类更大的过程，其中包含 Lehmann 和 Romano [Ann.国家主义者。 33 (2005) 1138-1154]在该论文中假设的类似正相关条件下控制γ-FDP。我们在 Romano 和 Shaikh 中提供了更好的降压和升压程序替代方案 [IMS 讲座笔记 Monogr：Ser. 49 (2006a) 33-50，安。国家主义者。 34 (2006b) 1850-1873] 使用零 p 值的成对联合分布。我们概括了 gamma-FDP 的概念，使其适用于愿意容忍一些错误拒绝的情况，或者由于高度依赖性，一些错误拒绝是不可避免的，并提供了在两种不同情况下控制这种广义 gamma-FDP 的方法：（i）仅边际 p 值可用，（ii）边际 p 值以及空 p 值的常见成对联合分布可用，并假设对 p 值的正相关和任意相关条件每个场景。我们的理论发现得到了数值研究的支持。
The probability of false discovery proportion (FDP) exceeding gamma is an element of [0, 1), defined as gamma-FDP, has received much attention as a measure of false discoveries in multiple testing. Although this measure has received acceptance due to its relevance under dependency, not much progress has been made yet advancing its theory under such dependency in a nonasymptotic setting, which motivates our research in this article. We provide a larger class of procedures containing the stepup analog of, and hence more powerful than, the stepdown procedure in Lehmann and Romano [Ann. Statist. 33 (2005) 1138-1154] controlling the gamma-FDP under similar positive dependence condition assumed in that paper. We offer better alternatives of the stepdown and stepup procedures in Romano and Shaikh [IMS Lecture Notes Monogr: Ser. 49 (2006a) 33-50, Ann. Statist. 34 (2006b) 1850-1873] using pairwise joint distributions of the null p-values. We generalize the notion of gamma-FDP making it appropriate in situations where one is willing to tolerate a few false rejections or, due to high dependency, some false rejections are inevitable, and provide methods that control this generalized gamma-FDP in two different scenarios: (i) only the marginal p-values are available and (ii) the marginal p-values as well as the common pairwise joint distributions of the null p-values are available, and assuming both positive dependence and arbitrary dependence conditions on the p-values in each scenario. Our theoretical findings are being supported through numerical studies.