An indexed multivariate dispersion ordering based on the Hausdorff distance
A new multivariate dispersion ordering based on the Hausdorff distance between nonempty convex compact sets is proposed. This dispersion ordering depends on an index, whose purpose is to blur for each random vector the ball centered at its expected value, and with a radius equal to the index. So, on the basis of such an index, we consider a random set associated with each random vector and dispersion comparisons are established by means of the Hausdorff distance associated with the random sets. Different properties of the new dispersion ordering are stated as well as some characterization theorems. Possible relationships with other dispersion orderings are also studied. Finally, several examples are developed.
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Volume (Year): 97 (2006)
Issue (Month): 7 (August)
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- Giovagnoli, Alessandra & Wynn, H. P., 1995. "Multivariate dispersion orderings," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 325-332, March.
- Hiai, Fumio & Umegaki, Hisaharu, 1977. "Integrals, conditional expectations, and martingales of multivalued functions," Journal of Multivariate Analysis, Elsevier, vol. 7(1), pages 149-182, March.
- Rojo, Javier & He, Guo Zhong, 1991. "New properties and characterizations of the dispersive ordering," Statistics & Probability Letters, Elsevier, vol. 11(4), pages 365-372, April.
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