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Elementary multivariate rearrangements and stochastic dominance on a Fréchet class

  • Decancq, Koen

A Fréchet class collects all multivariate joint distribution functions that have the same marginals. Members of a Fréchet class only differ with respect to the interdependence between their marginals. In this paper, I study orders of interdependence on a Fréchet class using two multivariate generalizations of the bivariate rearrangement proposed by Epstein and Tanny (1980) [4] and Tchen (1980) [16]. I show how these multivariate rearrangements are underlying multivariate first order stochastic dominance in terms of the joint distribution function and the survival function. A combination of both rearrangements is shown to be equivalent to the concordance order proposed by Joe (1990) [9].

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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 147 (2012)
Issue (Month): 4 ()
Pages: 1450-1459

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Handle: RePEc:eee:jetheo:v:147:y:2012:i:4:p:1450-1459
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  1. Nikolay Nenovsky & S. Statev, 2006. "Introduction," Post-Print halshs-00260898, HAL.
  2. Meyer, Margaret & Strulovici, Bruno, 2012. "Increasing interdependence of multivariate distributions," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1460-1489.
  3. Marco Scarsini, 1988. "Dominance Conditions for Multivariate Utility Functions," Management Science, INFORMS, vol. 34(4), pages 454-460, April.
  4. D'Agostino, Marcello & Dardanoni, Valentino, 2009. "The measurement of rank mobility," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1783-1803, July.
  5. Marco Scarsini & Alfred Muller, 2000. "Some remarks on the supermodular order," Post-Print hal-00540239, HAL.
  6. Atkinson, Anthony B & Bourguignon, Francois, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," Review of Economic Studies, Wiley Blackwell, vol. 49(2), pages 183-201, April.
  7. Larry G. Epstein & Stephen M. Tanny, 1980. "Increasing Generalized Correlation: A Definition and Some Economic Consequences," Canadian Journal of Economics, Canadian Economics Association, vol. 13(1), pages 16-34, February.
  8. Patrick Moyes & Nicolas Gravel, 2007. "Ethically robust comprisons of distributions of two individual attributes," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00389601, HAL.
  9. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
  10. David A. Hennessy & Harvey E. Lapan, 2003. "A Definition of 'More Systematic Risk' with Some Welfare Implications," Economica, London School of Economics and Political Science, vol. 70(279), pages 493-507, 08.
  11. Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
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