Hessian orders and multinormal distributions - à paraître

Marco Scarsini () and Alessandro Arlotto
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Marco Scarsini: GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique, Dipartimento di Scienze Economiche e Aziendali - LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma]

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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 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.

Keywords: Hessian orders; Multivariate normal distribution; Convex cones; Dual space; Completely positive order (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (7)

Published in Journal of Multivariate Analysis, 2009, Vol. 100, pp. 2324-2330. ⟨10.1016/j.jmva.2009.03.009⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00542400

DOI: 10.1016/j.jmva.2009.03.009

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