论文标题
独立的椭圆形分布最小
Independent Elliptical Distributions Minimize Their $\mathcal{W}_2$ Wasserstein Distance from Independent Elliptical Distributions with the Same Density Generator
论文作者
论文摘要
此简短说明是在$ \ Mathcal {w} _2 $ Wasserstein距离上的属性上，该距离表明独立的椭圆形分布最小化其$ \ MATHCAL {W} _2 $ WASSERSTEIN距离与给定的具有相同密度生成器的独立椭圆形分布的距离。此外，当分布不一定是椭圆形时，我们研究了该属性在Gelbrich结合的含义。同时，我们还将结果推广到分布不是独立的情况下。本注释的主要目的是引用需要利用此属性或其含义的论文。
This short note is on a property of the $\mathcal{W}_2$ Wasserstein distance which indicates that independent elliptical distributions minimize their $\mathcal{W}_2$ Wasserstein distance from given independent elliptical distributions with the same density generators. Furthermore, we examine the implications of this property in the Gelbrich bound when the distributions are not necessarily elliptical. Meanwhile, we also generalize the results to the cases when the distributions are not independent. The primary purpose of this note is for the referencing of papers that need to make use of this property or its implications.
