Multidimensional inequalities and generalized quantile functions

Sinem Bas, Philippe Bich () and Alain Chateauneuf
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Sinem Bas: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Philippe Bich: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

PSE-Ecole d'économie de Paris (Postprint) from HAL

Abstract: In this paper, we extend the generalized Yaari's dual theory for multidimensional distributions, in the vein of Galichon and Henry's paper (Galichon and Henry in J Econ Theory 147:1501–1516, 2012). We show how a class of generalized quantiles—which encompasses Galichon and Henry's one or multivariate quantile transform [see Arjas and Lehtonen (Math Oper Res 3(3):205–223, 1978), O'Brien (Ann Prob 3(1):80–88, 1975) or Ruschendorf (Ann Probab 9(2):276–283, 1981)]—allows to derive a general representation theorem.

Keywords: Multidimensional distributions; Quantile; Inequality; Optimal coupling (search for similar items in EconPapers)
Date: 2021-03
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Published in Economic Theory, 2021, 71, pp.375-409. ⟨10.1007/s00199-020-01253-5⟩

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Related works:
Journal Article: Multidimensional inequalities and generalized quantile functions (2021)
Working Paper: Multidimensional inequalities and generalized quantile functions (2021)
Working Paper: Multidimensional inequalities and generalized quantile functions (2021)
Working Paper: Multidimensional inequalities and generalized quantile functions (2016)
Working Paper: Multidimensional inequalities and generalized quantile functions (2016)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:pseptp:halshs-03029860

DOI: 10.1007/s00199-020-01253-5

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