In qualitative statistics, permutation tests are very popular, mainly because of their finite-sample exactness under exchangeability. However, in non-exchangeable settings, the covariance structure of permuted statistics typically differs from that of the original statistic. A common solution is studentization, which restores asymptotic correctness for general hypotheses while preserving exactness under exchangeability. In multiple testing settings, however, standard studentization fails to provide the correct joint limiting distribution. Existing solutions such as prepivoting address this issue but are computationally expensive and therefore rarely used in practice. We propose a general, computationally more efficient methodology that overcomes this fundamental limitation. By appropriately correcting the covariance matrix of multiple permutation statistics, our approach restores the correct joint asymptotic dependence structure, enabling asymptotically valid permutation tests in broad multiple testing frameworks. The proposed method is highly flexible: it accommodates singular covariance structures and is not tied to specific parameters, test statistics, or permutation schemes. This generality makes it applicable across a wide range of problems. Extensive simulation studies demonstrate that our approach results in reliable inference and outperforms existing methods across diverse settings.

翻译：在定性统计学中，置换检验因其在可交换性假设下具有有限样本精确性而广受欢迎。然而，在非可交换情形下，置换统计量的协方差结构通常与原统计量不同。常见解决方案是学生化方法，该方法能在保持可交换性下精确性的同时，恢复一般假设检验的渐近正确性。但在多重检验场景中，标准学生化方法无法提供正确的联合极限分布。现有如预枢轴化等方法虽能解决此问题，但计算成本过高，实践中极少使用。我们提出一种通用且计算效率更高的方法，突破了这一根本性局限。通过适当校正多重置换统计量的协方差矩阵，本方法能恢复正确的联合渐近相依结构，从而在广泛的多重检验框架下实现渐近有效的置换检验。所提方法灵活性极高：既能容纳奇异协方差结构，又不局限于特定参数、检验统计量或置换方案。这种普适性使其可应用于各类问题。大规模模拟研究证明，本方法能获得可靠的推断结果，并在多种场景下显著优于现有方法。