On the n-Coupling Problem

Ludger Rüschendorf and Ludger Uckelmann

Journal of Multivariate Analysis, 2002, vol. 81, issue 2, 242-258

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.

Keywords: optimal; couplings; multivariate; normal; distribution; measures; with; given; marginals (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (7)

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