标题： 渐近相依下的重尾组合检验的有效性与功效 显示英文标题

标题： Validity and Power of Heavy-Tailed Combination Tests under Asymptotic Dependence

摘要： 重尾组合检验，如柯西组合检验和调和平均p值方法，被广泛用于通过聚合相关p值来检验全局空假设。 然而，在一般依赖结构下的理论保证仍然有限。 我们开发了一个统一的框架，使用多变量正则变化的copula来模拟p值在零附近的联合行为。 在这个框架中，我们证明当变换分布具有尾指数$\gamma \leq 1$时，组合检验仍然是渐近有效的，其中$\gamma = 1$最大化功效同时保持有效性。 当$\gamma \to 0$时，邦弗朗尼检验成为极限情况，并在渐近依赖下变得过于保守。 因此，当p值表现出更强的下尾依赖性且信号不是极其稀疏时，具有$\gamma = 1$的组合检验相对于邦弗朗尼能实现渐进功效的提升。 我们的结果为使用截断柯西或帕累托组合检验提供了理论支持，在复杂依赖条件下提供了一种增强功效同时控制假阳性的合理方法。 显示英文摘要

摘要： Heavy-tailed combination tests, such as the Cauchy combination test and harmonic mean p-value method, are widely used for testing global null hypotheses by aggregating dependent p-values. However, their theoretical guarantees under general dependence structures remain limited. We develop a unified framework using multivariate regularly varying copulas to model the joint behavior of p-values near zero. Within this framework, we show that combination tests remain asymptotically valid when the transformation distribution has a tail index $\gamma \leq 1$, with $\gamma = 1$ maximizing power while preserving validity. The Bonferroni test emerges as a limiting case when $\gamma \to 0$ and becomes overly conservative under asymptotic dependence. Consequently, combination tests with $\gamma = 1$ achieve increasing asymptotic power gains over Bonferroni as p-values exhibit stronger lower-tail dependence and signals are not extremely sparse. Our results provide theoretical support for using truncated Cauchy or Pareto combination tests, offering a principled approach to enhance power while controlling false positives under complex dependence.