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• W2753373081 abstract "The improved Fr'echet--Hoeffding bounds are ad-hoc estimates on the Fr'echet class of probability distributions with given marginals and prescribed values on a subset of R d . Using an optimal transport approach, we first provide an alternative derivation of the improved upper bound. To this end, we establish a dual representation of a constrained transport problem over distributions in the aforementioned Fr'echet class and show that the improved upper Fr'echet--Hoeffding bound belongs to the class of admissible functions for the dual optimization problem. The proof of strong duality is based on a general representation result for increasing convex functionals and the explicit computation of the conjugates. We show further that the improved upper Fr'echet--Hoeffding bound is not the dual optimizer of this transport problem. In turn we prove that the improved upper bound is the dual optimizer of a relaxed version of the initial transport problem, thus proving sharpness of the improved upper Fr'echet--Hoeffding bound for the relaxed Fr'echet class. This is achieved by direct construction of the dual optimizers for a certain class of objective functions." @default.
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• W2753373081 date "2017-09-02" @default.
• W2753373081 modified "2023-09-27" @default.
• W2753373081 title "Sharpness of improved Fr'echet-Hoeffding bounds: an optimal transport approach" @default.
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