Joint mixability and negative orthant dependence
Joint mixability and negative orthant dependence
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发表时间：
2022
影响因子：
22.1
通讯作者：
Takaaki Koike;Liyuan Lin;Ruodu Wang
中科院分区：
文献类型：
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作者：
Takaaki Koike;Liyuan Lin;Ruodu Wang
联合混合是具有恒定分量和的随机向量。已知它表示某些公共目标的最小化相关结构，但它通常被认为是极值负相关的概念。在本文中，我们探讨了联合混合结构和统计学中最流行的负相关概念之一，称为负正交相关（NOD）之间的联系。我们表明，联合混合并不总是有NOD，但一些自然类的联合混合。特别是，高斯类被描述为唯一支持任意维度NOD联合混合的椭圆类。对于高斯边界，我们还得到了NOD联合混合存在的一个充要条件。最后，对于相同的边际分布，我们表明，NOD高斯联合混合解决了一个多边际的最优运输问题下的不确定性的组件的数量。分析这种具有异质边际的最优运输问题，揭示了NOD和联合混合结构之间的权衡。
A joint mix is a random vector with a constant component-wise sum. It is known to represent the minimizing dependence structure of some common objectives, and it is usu-ally regarded as a concept of extremal negative dependence. In this paper, we explore the connection between the joint mix structure and one of the most popular notions of negative dependence in statistics, called negative orthant dependence (NOD). We show that a joint mix does not always have NOD, but some natural classes of joint mixes have. In particular, the Gaussian class is characterized as the only elliptical class which supports NOD joint mixes of arbitrary dimension. For Gaussian margins, we also derive a necessary and sufficient condition for the existence of an NOD joint mix. Finally, for identical marginal distributions, we show that an NOD Gaussian joint mix solves a multi-marginal optimal transport problem under uncertainty on the number of components. Analysis of this optimal transport problem with heterogeneous marginals reveals a trade-off between NOD and the joint mix structure.