Zonoids, Linear Dependence, and Size-Biased Distributions on the Simplex
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 characterizes 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.
|Date of creation:||Dec 2000|
|Date of revision:||Jul 2003|
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- Marco Scarsini & Marco Dall'Aglio, 2001.
"When Lorenz met Lyapunov,"
- Koshevoy, Gleb & Mosler, Karl, 1995.
"Multivariate Gini indices,"
Discussion Papers in Econometrics and Statistics
7/95, University of Cologne, Institute of Econometrics and Statistics.
- Machina, Mark J & Pratt, John W, 1997. "Increasing Risk: Some Direct Constructions," Journal of Risk and Uncertainty, Springer, vol. 14(2), pages 103-127, March.
- K. Mosler, 2003. "Central regions and dependency," Econometrics 0309004, EconWPA.
- Gleb Koshevoy, 1997. "The Lorenz zonotope and multivariate majorizations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(1), pages 1-14.
- Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
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