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A stochastic order for random vectors and random sets based on the Aumann expectation

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  • Fernández, Ignacio Cascos
  • Molchanov, Ilya

Abstract

We define a new stochastic order for random vectors in terms of the inclusion relation for the Aumann expectation of certain random sets. We derive some properties of this order, relate it with other well-known multivariate stochastic convex orders, give a geometrical interpretation in terms of the lift zonoid, build a probability metric based on it and extend it to compare random compact sets. Furthermore, a new characterisation of the linear convex order for random vectors is described and the corresponding concept is extended to compare random compact sets.

Suggested Citation

  • Fernández, Ignacio Cascos & Molchanov, Ilya, 2003. "A stochastic order for random vectors and random sets based on the Aumann expectation," Statistics & Probability Letters, Elsevier, vol. 63(3), pages 295-305, July.
    • Handle: RePEc:eee:stapro:v:63:y:2003:i:3:p:295-305
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    References listed on IDEAS

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    1. Marco Scarsini, 1998. "Multivariate convex orderings, dependence, and stochastic equality," Post-Print hal-00541775, HAL.
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    Cited by:

    1. Cascos, Ignacio & López-Díaz, Miguel, 2005. "Integral trimmed regions," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 404-424, October.
    2. Belaid AOUNI & Cinzia COLAPINTO & Davide LA TORRE, 2008. "Solving stochastic multi-objective programming through the GP model," Departmental Working Papers 2008-18, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.

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