发表机构
University of Science and Technology of China; Zhengzhou University（中国科学技术大学; 郑州大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对弱矩条件下的两样本分布相等性检验问题，提出基于多次积分分位数度量的新检验方法，该方法仅需有限一阶矩，通过模拟与实际数据验证其性能。
AI 中文摘要
检验两个独立样本是否源自同一基础分布是一个基础统计问题。我们提出一类新的两样本分布检验方法，基于由多次积分分位数函数构造的概率度量族Δ_{n,p}，在各自定义域内，这些度量被证明是真实的分布距离。当n=1时，该度量退化为p-沃瑟斯坦距离，其要求存在有限的p阶矩；对于n≥2，所提出的度量有明确定义且仅要求存在有限的一阶矩。我们建立了插件统计量的渐近性质，包括原假设和固定备择假设下的强一致性与极限分布，还提出了有限样本推断的置换校准方法，进一步推导了局部备择假设下的渐近功效函数。最后，通过模拟研究检验了所提检验的有限样本性能，并通过实际数据应用展示了其对极端上尾观测值的敏感性较低。
英文摘要
Testing whether two independent samples arise from the same underlying distribution is a fundamental statistical problem. We propose a new class of two-sample distribution tests based on a family of probability metrics $Δ_{n,p}$, constructed from repeatedly integrated quantile functions. On their respective domains, these metrics are proved to be genuine distributional distances. The case $n=1$ recovers the $p$-Wasserstein distance, which requires finite $p$-th moments; for $n\geq2$, the proposed metrics are well defined and require only finite first moments. The asymptotic properties of the plug-in statistic are established, including strong consistency and limiting distributions under the null and fixed alternatives. A permutation calibration for finite-sample inference is also proposed. We further derive an asymptotic power function under local alternatives. Finally, the finite-sample performance of the proposed tests is examined through simulation studies, and their reduced sensitivity to extreme upper-tail observations is illustrated through a real data application.
