Approximation to Probabilities Through Uniform Laws on Convex Sets

J. A. Cuesta-Albertos (), C. Matrán and J. Rodríguez-Rodríguez
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J. A. Cuesta-Albertos: Universidad de Cantabria
C. Matrán: Universidad de Valladolid
J. Rodríguez-Rodríguez: Universidad de Valladolid

Journal of Theoretical Probability, 2003, vol. 16, issue 2, 363-376

Abstract: Abstract Let P be a probability distribution on ∝ d and let $$C$$ be the family of the uniform probabilities defined on compact convex sets of ∝ d with interior non-empty. We prove that there exists a best approximation to P in $$C$$ , based on the L 2-Wasserstein distance. The approximation can be considered as the best representation of P by a convex set in the minimum squares setting, improving on other existent representations for the shape of a distribution. As a by-product we obtain properties related to the limit behavior and marginals of uniform distributions on convex sets which can be of independent interest.

Keywords: Wasserstein distance; uniform laws; convex sets; existence (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1023/A:1023518526754

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