双向高斯均值检验中的依赖意识虚假发现率控制
Dependence-Aware False Discovery Rate Control in Two-Sided Gaussian Mean Testing
AI总结：
本文提出了一种基于正左尾依赖性的改进方法，用于在双向高斯均值检验中更有效地控制虚假发现率。
摘要：
本文开发了一个通用框架，用于在高斯均值的多重检验中控制虚假发现率（FDR）。广泛使用的Benjamini-Hochberg（BH）程序在独立或保守控制下提供精确的FDR控制，但在相关双向检验中的有效性仍是一个开放问题。我们引入了在原假设下的正左尾依赖性（PLTDN）的概念，将经典依赖假设扩展到双向设置，并证明其确保了BH型程序的FDR控制有效性。基于此框架，我们提出了一族广义移位BH（GSBH）方法，通过简单的p值调整整合相关性信息。模拟结果表明，该方法在各种依赖结构中都能提供可靠的FDR控制和改进的统计功效，而对HIV基因表达数据集的应用展示了所提出方法的实用性。
英文摘要：
This paper develops a general framework for controlling the false discovery rate (FDR) in multiple testing of Gaussian means against two-sided alternatives. The widely used Benjamini-Hochberg (BH) procedure provides exact FDR control under independence or conservative control under specific one-sided dependence structures, but its validity for correlated two-sided tests has remained an open question. We introduce the notion of positive left-tail dependence under the null (PLTDN), extending classical dependence assumptions to two-sided settings, and show that it ensures valid FDR control for BH-type procedures. Building on this framework, we propose a family of generalized shifted BH (GSBH) methods that incorporate correlation information through simple p-value adjustments. Simulation results demonstrate reliable FDR control and improved power across a range of dependence structures, while an application to an HIV gene expression dataset illustrates the practical effectiveness of the proposed approach.
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