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Linkages: A Tool for the Construction of Multivariate Distributions with Given Nonoverlapping Multivariate Marginals

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  • Li, Haijun
  • Scarsini, Marco
  • Shaked, Moshe

Abstract

One of the most useful tools for handling multivariate distributions with givenunivariatemarginals is the copula function. Using it, any multivariate distribution function can be represented in a way that emphasizes the separate roles of the marginals and of the dependence structure. The goal of the present paper is to introduce an analogous tool, called the linkage function, that can be used for the study of multivariate distributions with givenmultivariatemarginals by emphasizing the separate roles of the dependence structurebetweenthe given multivariate marginals, and the dependence structurewithineach of the nonoverlapping marginals. Preservation of some setwise positive dependence properties, from the linkage functionLto the joint distributionFand vice versa, are studied. When two different distribution functions are associated with the same linkage function (that is, have the same setwise dependence structure) we show that strong stochastic dominance order among the corresponding multivariate marginal distributions implies an overall stochastic dominance between the two underlying distribution functions.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 56 (1996)
Issue (Month): 1 (January)
Pages: 20-41

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Handle: RePEc:eee:jmvana:v:56:y:1996:i:1:p:20-41

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Related research

Keywords: copula given marginals dependence structure setwise positive dependence stochastic order standard construction;

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Cited by:
  1. Sancetta, A. & Nikanrova, A., 2005. "Forecasting and Prequential Validation for Time Varying Meta-Elliptical Distributions with a Study of Commodity Futures Prices," Cambridge Working Papers in Economics 0516, Faculty of Economics, University of Cambridge.
  2. Ramkishen S. Rejan, 1998. "The Currency And Financial Crisis In Southeast Asia - A Case Of `Sudden Deathã¢Â‚¬Â„¢ Or `Death Foretoldã¢Â‚¬Â„¢," Macroeconomics Working Papers 22381, East Asian Bureau of Economic Research.
  3. Li, Haijun & Scarsini, Marco & Shaked, Moshe, 1999. "Dynamic Linkages for Multivariate Distributions with Given Nonoverlapping Multivariate Marginals," Journal of Multivariate Analysis, Elsevier, vol. 68(1), pages 54-77, January.
  4. Alessio Sancetta, 2004. "Copula Based Monte Carlo Integration in Financial Problems," Working Papers wp04-02, Warwick Business School, Finance Group.
  5. Kaiser, Mark S. & Cressie, Noel, 2000. "The Construction of Multivariate Distributions from Markov Random Fields," Journal of Multivariate Analysis, Elsevier, vol. 73(2), pages 199-220, May.
  6. Bairamov, Ismihan & Khaledi, Baha-Eldin & Shaked, Moshe, 2014. "Stochastic comparisons of order statistics and their concomitants," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 105-115.
  7. Belzunce, Félix & Ruiz, José M. & Suárez-Llorens, Alfonso, 2008. "On multivariate dispersion orderings based on the standard construction," Statistics & Probability Letters, Elsevier, vol. 78(3), pages 271-281, February.

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