论文标题
在负依赖性下进行多次测试
Multiple testing under negative dependence
论文作者
论文摘要
多个测试文献主要涉及p值之间的三种依赖性假设：独立性，积极回归依赖性和任意依赖性。在本文中，我们认为我们认为是负依赖性各种概念（负依赖性，负回归依赖性，负相关，负相关性和弱负依赖性）下的第一个理论结果。其中包括模拟全局无效测试和本杰米尼·霍赫伯格（Benjamini-Hochberg）程序，在实验上已知在负依赖性下是抗保守性的。这些程序的抗保守性是由小于任意依赖性（尤其是由与假设数量的因素）小的因素界定的。我们还提供了有关负依赖的电子价值的新结果，并提供了几个示例，涉及何时出现负面依赖性。我们的证明是基本的，很短，因此可以适合扩展。
The multiple testing literature has primarily dealt with three types of dependence assumptions between p-values: independence, positive regression dependence, and arbitrary dependence. In this paper, we provide what we believe are the first theoretical results under various notions of negative dependence (negative Gaussian dependence, negative regression dependence, negative association, negative orthant dependence and weak negative dependence). These include the Simes global null test and the Benjamini-Hochberg procedure, which are known experimentally to be anti-conservative under negative dependence. The anti-conservativeness of these procedures is bounded by factors smaller than that under arbitrary dependence (in particular, by factors independent of the number of hypotheses). We also provide new results about negatively dependent e-values, and provide several examples as to when negative dependence may arise. Our proofs are elementary and short, thus amenable to extensions.
