Some remarks on the supermodular order

Marco Scarsini and Alfred Müller

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Abstract: In this paper we solve two open problems posed by Joe (1997) concerning the supermodular order. First we give an example which shows that the supermodular order is strictly stronger than the concordance order for dimension d=3. Second we show that the supermodular order fulfils all desirable properties of a multivariate positive dependence order. We especially prove the non-trivial fact that it is closed with respect to weak convergence. This is applied to give a complete characterization of the supermodular order for multivariate normal distributions.

Keywords: dependence orders; supermodular order; L-superadditive functions; weak convergence; concordance (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (53)

Published in Journal of Multivariate Analysis, 2000, Vol. 73, N°1, pp. 107-119. ⟨10.1006/jmva.1999.1867⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00540239

DOI: 10.1006/jmva.1999.1867

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