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.

翻译：本文提出了一个用于控制双侧备择假设下高斯均值多重检验中错误发现率（FDR）的通用框架。广泛使用的Benjamini-Hochberg（BH）方法在独立性假设下能提供精确的FDR控制，或在特定单侧依赖结构下提供保守控制，但其在相关双侧检验中的有效性一直是一个开放性问题。我们引入了零假设下正左尾依赖（PLTDN）的概念，将经典依赖假设扩展至双侧检验场景，并证明该条件能确保BH类方法的有效FDR控制。基于此框架，我们提出了一族广义平移BH（GSBH）方法，通过简单的p值调整融入相关性信息。仿真结果表明，该方法在多种依赖结构下均能实现可靠的FDR控制并提升检验功效，而在HIV基因表达数据集中的应用进一步验证了所提方法的实际有效性。