标题： 通过利用任意协方差结构增强信号比例估计 显示英文标题

标题： Enhancing Signal Proportion Estimation Through Leveraging Arbitrary Covariance Structures

摘要： 准确估计大量变量中真实信号的比例对于提高科学研究的精度和可靠性至关重要。 传统的信号比例估计器通常假设变量之间相互独立并具有特定的信号稀疏性条件，这限制了它们在现实场景中的适用性，因为在这些场景中这些假设可能不成立。 本文介绍了一种新的信号比例估计器，该估计器利用变量之间的任意协方差依赖信息，从而在广泛的稀疏性水平和依赖结构下提高性能。 在之前提供信号比例下限置信区间的工作基础上，我们通过引入主因子近似程序来考虑变量依赖性，扩展了这一方法。 我们的理论见解提供了对信号稀疏性、信号强度和协方差依赖性之间相互作用的更深入理解。 通过比较调整依赖性前后的估计一致性条件，我们突出了在不同情境中整合依赖信息的优势。 这一理论基础不仅验证了新估计器的有效性，还指导了其实际应用，确保在各种场景中可靠使用。 通过大量的模拟实验，我们证明了我们的方法在估计精度和检测较弱信号方面优于最先进的估计器，这些较弱信号可能 otherwise 被忽略。 显示英文摘要

摘要： Accurately estimating the proportion of true signals among a large number of variables is crucial for enhancing the precision and reliability of scientific research. Traditional signal proportion estimators often assume independence among variables and specific signal sparsity conditions, limiting their applicability in real-world scenarios where such assumptions may not hold. This paper introduces a novel signal proportion estimator that leverages arbitrary covariance dependence information among variables, thereby improving performance across a wide range of sparsity levels and dependence structures. Building on previous work that provides lower confidence bounds for signal proportions, we extend this approach by incorporating the principal factor approximation procedure to account for variable dependence. Our theoretical insights offer a deeper understanding of how signal sparsity, signal intensity, and covariance dependence interact. By comparing the conditions for estimation consistency before and after dependence adjustment, we highlight the advantages of integrating dependence information across different contexts. This theoretical foundation not only validates the effectiveness of the new estimator but also guides its practical application, ensuring reliable use in diverse scenarios. Through extensive simulations, we demonstrate that our method outperforms state-of-the-art estimators in both estimation accuracy and the detection of weaker signals that might otherwise go undetected.