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On the n-Coupling Problem

✍ Scribed by Ludger Rüschendorf; Ludger Uckelmann

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
148 KB
Volume
81
Category
Article
ISSN
0047-259X

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✦ Synopsis

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.

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