解析高维准耦合器质量分布极值，解决关键开放问题
Extreme mass distributions for quasi-copulas
- 采用解析方法求解多维准耦合器质量分布极值
- 完全解答原始问题，推翻近期一个猜想，验证至17维
- 适合依赖建模与概率统计研究者阅读
近期综述《星际漫游指南》（Hitchhiker's Guide）虽未赋予准耦合器明确的统计解释，但提升了其在依赖建模领域的关注度。我们此前通过线性规划方法，解决了该指南中第5个开放问题，直至维度d=17，并推翻了关于该问题解的一个新猜想。本文采用解析方法，给出了该原始问题的完整解答。
原文摘要 · Abstract (English)
A recent survey, nicknamed "Hitchhiker's Guide", J.J. Arias-Garcıa, R. Mesiar, and B. De Baets, A hitchhiker's guide to quasi-copulas, Fuzzy Sets and Systems 393 (2020) 1-28, has raised the rating of quasi-copula problems in the dependence modeling community in spite of the lack of statistical interpretation of quasi-copulas. In our previous work (Fuzzy Sets and Systems 517 (2025) 109457), we addressed the question of extreme values of the mass distribution associated with multivariate quasi-copulas. Using a linear programming approach, we were able to solve Open Problem 5 of the "Guide" up to dimension d = 17 and disprove a recent conjecture on the solution to that problem. In this paper, we use an analytical approach to provide a complete answer to the original question.
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