On the n-coupling problem

Authors:
Ludger Rüschendorf;Ludger Uckelmann
Affiliations:
University of Freiburg, Freiburg, Germany;University of Freiburg, Freiburg, Germany
Venue:
Journal of Multivariate Analysis
Year:
2002

Citing 3
Cited 1

A characterization of random variables with minimum L2-distance

Journal of Multivariate Analysis
Maximum submatrix traces for positive definite matrices

SIAM Journal on Matrix Analysis and Applications
On the n-coupling problem

Journal of Multivariate Analysis

On the n-coupling problem

Journal of Multivariate Analysis

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Abstract

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.