On the n-coupling problem

被引：37

作者：

Rüschendorf, L ^{[1
]}

Uckelmann, L ^{[1
]}

机构：

[1] Univ Freiburg, Freiburg, Germany

来源：

JOURNAL OF MULTIVARIATE ANALYSIS | 2002年 / 81卷 / 02期

关键词：

optimal couplings; multivariate normal distribution; measures with given marginals;

D O I：

10.1006/jmva.2001.2005

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper we obtain based on an idea of M. Knott and C. S. Smith (1994, Linear Algebra Appl. 199, 363-371) characterizations of solutions of three-coupling problems by reduction to the construction of optimal couplings of each of the variables to the sum. In the case of normal distributions this leads to a complete solution. Under a technical condition this idea also works for general distributions and one obtains explicit results. We extend these results to the n-coupling problem and derive a characterization of optimal n-couplings by several 2-coupling problems. This leads to some constructive existence results for Monge solutions. (C) 2002 Elsevier Science (USA).

引用

页码：242 / 258

页数：17

共 18 条

[1] ON THE STRUCTURE OF SINGULAR SETS OF CONVEX-FUNCTIONS [J].