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Hessian orders and multinormal distributions

Abstract : Several well known integral stochastic orders (like the convex order, the supermodular order, etc.) can be defined in terms of the Hessian matrix of a class of functions. Here we consider a generic Hessian order, i.e., an integral stochastic order defined through a convex cone of Hessian matrices, and we prove that if two random vectors are ordered by the Hessian order, then their means are equal and the difference of their covariance matrices belongs to the dual of H. Then we show that the same conditions are also sufficient for multinormal random vectors. We study several particular cases of this general result.
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https://hal-hec.archives-ouvertes.fr/hal-00491679
Contributor : Antoine Haldemann <>
Submitted on : Monday, June 14, 2010 - 10:17:58 AM
Last modification on : Thursday, January 11, 2018 - 6:19:31 AM

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Marco Scarsini, Alexandro Arlotto. Hessian orders and multinormal distributions. Journal of Multivariate Analysis, Elsevier, 2009, Vol.100,nº10, pp.2324-2330. ⟨10.1016/j.jmva.2009.03.009⟩. ⟨hal-00491679⟩

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