通过限制置换为块内单次交换，提升两样本检验的统计功效。
Restricted Block Permutation for Two-Sample Testing
- 采用块选择代表元素间的单次交叉置换，构造精确有效方法。
- 置换增量方差降为O(h²)，显著降低临界值，提升检验力。
- 无需保守假设，适用于追求高精度的小样本检验场景。
我们研究一种用于两样本检验的结构化置换方案，将置换限制为块选取代表之间的单次交叉交换。分析得出三个主要结果：第一，给出了适用于任意固定受限置换集的精确有效性构造；第二，针对样本均值之差和无偏 $\ ext{MMD}^2$ 估计量，推导出闭式单交换增量恒等式，其条件方差缩放为 $O(h^2)$，远优于全重标记下的 $Θ(h)$ 增量变异性；该增量级方差收缩优化了 Bernstein--Freedman 方差代理，使置换临界值显著减小；第三，得到了结果临界值与统计功效的显式、数据依赖表达式。综合表明，块受限单交换置换可在保持精确有限样本有效性的同时，实现严格高于经典全置换检验的统计功效，且不依赖于悲观的最坏情况 Lipschitz 界。
原文摘要 · Abstract (English)
We study a structured permutation scheme for two-sample testing that restricts permutations to single cross-swaps between block-selected representatives. Our analysis yields three main results. First, we provide an exact validity construction that applies to any fixed restricted permutation set. Second, for both the difference of sample means and the unbiased $\widehat{\mathrm{MMD}}^{2}$ estimator, we derive closed-form one-swap increment identities whose conditional variances scale as $O(h^{2})$, in contrast to the $Θ(h)$ increment variability under full relabeling. This increment-level variance contraction sharpens the Bernstein--Freedman variance proxy and leads to substantially smaller permutation critical values. Third, we obtain explicit, data-dependent expressions for the resulting critical values and statistical power. Together, these results show that block-restricted one-swap permutations can achieve strictly higher power than classical full permutation tests while maintaining exact finite-sample validity, without relying on pessimistic worst-case Lipschitz bounds.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。