发表机构
University of Central Florida（中佛罗里达大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出omega-1无分布拟合优度检验，作为Kolmogorov--Smirnov等检验的线性类似物，推导其有限维计算形式与极限分布，经模拟验证收敛快、适用性强。
AI 中文摘要
我们引入一种名为omega-1检验的无分布拟合优度检验，它是Kolmogorov--Smirnov检验和Cramér--von Mises检验的自然补充，可视为它们的（分段）线性类似物。该检验统计量定义为经验过程的L¹泛函，在平衡对局部替代和弥散替代的敏感性方面有所改进，提供了稳健且可解释的分布差异度量，且与Wasserstein 1距离密切相关。对于有限样本，我们在一般条件下推导了该统计量的有限维计算形式，由此得到其原分布的多种显式公式。在温和的连续性假设下，极限统计量是无分布的，具有显式分布公式。在复合场景中，该统计量也与Khmaladze变换兼容，可实现渐近无分布检验。极限变换后的统计量同样具有显式分布，无需依赖难以处理的补偿过程或纯数值评估。模拟结果表明，有限样本分布向其极限分布收敛迅速，支持该检验的实际适用性。
英文摘要
We introduce a distribution-free goodness-of-fit test, termed the omega-1 test, which naturally complements the Kolmogorov--Smirnov test and Cramér--von Mises test and can be viewed as their (piecewise) linear analog. Defined as an $\mathrm{L}^{1}$-functional of the empirical process, the test statistic improves on balancing sensitivity to localized and diffuse alternatives and gives a robust and interpretable measure of distributional discrepancy, apart from close connections to the Wasserstein 1-distance. For finite samples, we derive a finite-dimensional computational form for the statistic under general conditions, which leads to various explicit formulas for its null distribution. Under mild continuity assumptions, the limiting statistic is distribution-free, with explicit distribution formulas. In composite settings, the statistic is also compatible with the Khmaladze transformation, enabling asymptotically distribution-free testing. The limiting transformed statistic also has an explicit distribution that escapes reliance on intractable compensator processes or purely numerical evaluation. Simulation results indicate rapid convergence of the finite-sample distributions to their limiting counterparts and support the practical applicability of the test.
Comments20 pages, 1 table, 3 figures
