Hessian orders and multinormal distributions

JOURNAL OF MULTIVARIATE ANALYSIS

卷:100

Article

Arlotto, Alessandro¹  Scarsini, Marco^2,3 

[1] Univ Penn, Wharton Sch, OPIM Dept, Philadelphia, PA 19104 USA

[2] LUISS, Dipartimento Sci Econ & Aziendali, I-00197 Rome, Italy

[3] HEC, Paris, France

关键词: Hessian orders;    Multivariate normal distribution;    Convex cones;    Dual space;    Completely positive order;   

DOI  :  10.1016/j.jmva.2009.03.009

来源: Elsevier

【 摘 要 】

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 H 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. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free