发表机构
School of Management, University of Science and Technology of China; Guanghua School of Management, Peking University（中国科学技术大学管理学院; 北京大学光华管理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于Copula导数的检验方法，用于在共同协变量值下比较两个总体的条件分布，实现一阶随机占优的同时推断，并通过模拟和PSID应用验证其有效性。
AI 中文摘要
在相同的物理协变量值下比较两个总体，需要的不仅仅是条件均值或孤立的目标点决策：研究人员可能需要关于整个条件分布排序在连续区间上的证据，即使协变量边缘分布不同。本文在明确的灵活性-权衡结构下使这种共同值比较可估计，并将所得曲面转化为一阶随机占优的同时证据。总体特定的边缘分布将共同协变量值映射到每个组，而拟合的Copula导数表示则连接整个区域的条件分布。均匀推断通过一个具有未知绑定位置的单侧统计量，将来自边缘分布和依赖模型的不确定性传播开来。在有限Copula类内的正确设定、光滑性和修剪条件以及唯一最优候选族下，该过程实现了均匀控制和一致的校准。模拟显示，随着备择假设变得更加可区分，拒绝率增加，同时存在模型选择敏感性和小样本尺寸失真。在一个描述性的PSID应用中，高-低父母教育比较在多重性调整后满足双向标准，而相邻教育组的比较仍不明确。因此，该框架支持区域范围的分布比较，同时明确其结构和推断边界。
英文摘要
Comparing two populations at the same physical covariate value requires more than conditional means or isolated target-point decisions: researchers may need evidence about an entire conditional-distribution ordering over a continuum, even when covariate margins differ. This paper makes that common-value comparison estimable under an explicit structure--flexibility tradeoff and turns the resulting surface into simultaneous evidence for first-order stochastic dominance. Population-specific margins map the common covariate value into each group, while a fitted copula-derivative representation links conditional distributions across the region. Uniform inference propagates uncertainty from both the margins and dependence model through a one-sided statistic with unknown binding locations. Under correct specification within a finite copula class, smoothness and trimming conditions, and a uniquely best candidate family, the procedure admits uniform control and consistent calibration. Simulations show increasing rejection as alternatives become more distinguishable, alongside model-selection sensitivity and small-sample size distortion. In a descriptive PSID application, the high--low parental-education comparison satisfies the two-direction criterion after multiplicity adjustment, whereas adjacent education-group comparisons remain inconclusive. The framework therefore supports region-wide distributional comparison while making its structural and inferential boundaries explicit.
