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Zonoids, Linear Dependence, and Size-Biased Distributions on the Simplex

Abstract : The zonoid of a d-dimensional random vector is used as a tool for measuring linear dependence among its components. A preorder of linear dependence is defined through inclusion of the zonoids. The zonoid of a random vector does not characterize its distribution, but it does characterize the size-biased distribution of its compositional variables. This fact will allow a characterization of our linear dependence order in terms of a linear-convex order for the size-biased compositional variables. In dimension 2 the linear dependence preorder will be shown to be weaker than the concordance order. Some examples related to the Marshall-Olkin distribution and to a copula model will be presented, and a class of measures of linear dependence will be proposed.
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Submitted on : Thursday, November 25, 2010 - 11:00:51 AM
Last modification on : Thursday, January 11, 2018 - 6:19:31 AM

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Marco Scarsini, Marco Dall'Aglio. Zonoids, Linear Dependence, and Size-Biased Distributions on the Simplex. Advances in Applied Probability, Applied Probability Trust, 2003, Vol. 34, N°4, pp. 871-884. ⟨10.1239/aap/1067436324⟩. ⟨hal-00539799⟩

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