Effectively controlling the false discovery rate (FDR) in high-dimensional variable selection is a fundamental statistical problem that has garnered significant research interest. In this paper, we propose a novel, user-friendly, and computationally efficient method called Bi-Gaussian Mirrors (BGM), which offers a conceptually simple yet powerful approach for FDR control. Our method makes the first attempt to achieve FDR control in high-dimensional data with complex dependencies, while overcoming key limitations of existing approaches, such as prior knowledge of the joint distribution of data, significant power loss, the need for full symmetry in test statistics, and the theoretical restriction to linear regression models. Additionally, we present a self-guiding procedure designed to enhance the practicality and applicability of the BGM method. Theoretical guarantees for FDR control and asymptotic power are rigorously established under regularity conditions. Moreover, extensive numerical simulations and two real-data examples demonstrate that the BGM method outperforms existing approaches in terms of finite-sample performance, achieving a superior balance between FDR control and testing power.

翻译：在高维变量选择中有效控制错误发现率（FDR）是一个基础统计问题，已引起广泛研究关注。本文提出一种新颖、用户友好且计算高效的方法——双高斯镜像法（BGM），它通过概念简洁而强大的方式实现FDR控制。该方法首次尝试在具有复杂依赖性的高维数据中实现FDR控制，同时克服了现有方法的关键局限，例如需要数据联合分布的先验知识、显著的功效损失、检验统计量需完全对称以及理论上仅限于线性回归模型。此外，我们提出一种自引导程序，旨在增强BGM方法的实用性和适用性。在正则条件下，严格建立了FDR控制与渐近功效的理论保证。广泛的数值模拟和两个实际数据示例表明，BGM方法在有限样本表现上优于现有方法，在FDR控制与检验功效之间实现了更优的平衡。