DIMACS TR: 2005-34
Monge Property and Bounding Multivariate Probability Distribution Functions with Given Marginals and Covariances
Authors: Xiaoling Hou and Andras Prekopa
Multivariate probability distributions with given marginals are considered, along with linear
functionals, to be minimized or maximized, acting on them. The functionals are supposed to satisfy
the Monge or inverse Monge or some higher order convexity property and they may
be only partially known.
Existing results in connection with Monge arrays are
reformulated and extended in terms of LP dual feasible bases. Lower and upper bounds are given
for the optimum value as well as for unknown coefficients of the objective function
based on the knowledge of some dual feasible basis and corresponding objective function coefficients.
In the two- and three-dimensional cases dual feasible bases are obtained for the problem, where
not only the univariate marginals, but also the covariances of the pairs of random
variables are known.
Distributions with given marginals, transportation problem, Monge arrays,
bounding expectations under partial information.
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