发表机构
The Pennsylvania State University（宾夕法尼亚州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对高维相依 $p$-值组合问题，提出统一渐近理论，解耦边际误差与联合相依结构，并给出维度增长率和相关率，确保极端显著性水平下全局检验的有限样本有效性。
AI 中文摘要
组合 $p$-值是全局假设检验中的基本程序。然而，在现代高维设定下，分量 $p$-值往往表现出复杂的相依性，并依赖于渐近近似而非精确的有限样本均匀分布。本文为加权变换统计量建立了一个统一的渐近理论，该理论将边际有限样本近似误差与联合相依结构解耦。我们还基于条件概率界提供了充分条件来验证联合尾部条件。利用这一框架，我们推导了在渐近高斯和卡方校准下运行的检验统计量的显式维度增长率和相关率。对于非精确的有限样本统计量，我们分析了标准化加权和，展示了 Cramér 中等偏差如何控制相对尾部误差。分析示例证明了为什么边际和联合条件对于相依性下的有效全局推断在数学上都是不可或缺的，数值实验证实了我们的渐近框架在极端显著性水平下能保持准确的有限样本大小控制。
英文摘要
Combining $p$-values is a fundamental procedure in global hypothesis testing. In modern high-dimensional settings, however, component $p$-values often exhibit complex dependence and rely on asymptotic approximations rather than exact finite-sample uniform distributions. This paper establishes a unified asymptotic theory for weighted transformation statistics that decouples marginal finite-sample approximation error from the joint dependence structure. We also provide sufficient conditions based on conditional probability bounds to verify the joint-tail conditions. Utilizing this framework, we derive explicit dimension-growth and correlation rates for test statistics operating under asymptotic Gaussian and chi-square calibrations. For non-exact finite-sample statistics, we analyze standardized weighted sums, demonstrating how Cramér moderate deviations control relative tail error. Analytical examples demonstrate why both marginal and joint conditions are mathematically indispensable for valid global inference under dependence, and numerical experiments confirm that our asymptotic framework maintains accurate finite-sample size control at extreme significance levels.
Comments23 pages, 5 tables
