论文标题
关节混合性和负依赖性的概念
Joint mixability and notions of negative dependence
论文作者
论文摘要
关节混合物是一个随机矢量，具有恒定的组分总和。关节混合物的依赖性结构最小化了一些共同的目标，例如组件总和的方差，它被认为是极端负依赖性的概念。在本文中，我们探讨了关节混合结构与统计中负依赖性的流行概念之间的联系，例如负相关依赖性，负矫正依赖性和负相关性。在上述任何一种感觉上，关节混合物并不总是负依赖，但是某些自然类的关节混合物是。我们得出了各种必要和足够的条件，使联合混合物具有负依赖性，并研究了这些概念的兼容性。对于相同的边际分布，我们表明，在新型的不确定性环境下，负面依赖的关节混合物解决了二次成本的多边界最佳运输问题。对这种最佳运输问题的分析与边际边缘的分析揭示了负依赖性与关节混合结构之间的权衡。
A joint mix is a random vector with a constant component-wise sum. The dependence structure of a joint mix minimizes some common objectives such as the variance of the component-wise sum, and it is regarded as a concept of extremal negative dependence. In this paper, we explore the connection between the joint mix structure and popular notions of negative dependence in statistics, such as negative correlation dependence, negative orthant dependence and negative association. A joint mix is not always negatively dependent in any of the above senses, but some natural classes of joint mixes are. We derive various necessary and sufficient conditions for a joint mix to be negatively dependent, and study the compatibility of these notions. For identical marginal distributions, we show that a negatively dependent joint mix solves a multi-marginal optimal transport problem for quadratic cost under a novel setting of uncertainty. Analysis of this optimal transport problem with heterogeneous marginals reveals a trade-off between negative dependence and the joint mix structure.
