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

✍ Scribed by Ignacio Cascos Fernández; Ilya Molchanov

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
222 KB
Volume
63
Category
Article
ISSN
0167-7152

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✦ Synopsis

We deÿne 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.

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