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Central regions and dependency


  • K. Mosler

    (Universität zu Köln)


The paper introduces an approach to the ordering of dependence which is based on central regions. A d-variate probability distribution is described by a nested family of sets, called central regions. Those regions are affine equivariant, compact and starshaped and concentrate about a properly defined center. They can be seen as level sets of a depth function. Special cases are Mahalanobis, zonoid, and likelihood regions. A d-variate distribution is called more dependent than another one if the volume of each central region is smaller with the first distribution. This dependence order is characterized by an inequality between determinants of certain parameter matrices if either (i) F and G are arbitrary distributions and the central regions are Mahalanobis or (ii) F and G belong to an elliptical family of distributions and the central regions are arbitrary. If the regions are zonoid regions, the dependence order implies the ordering of lift zonoid volumes. Alternatively, the dependence order is applied to the copulae of the given distributions. Generalized correlation indices are proposed which are increasing with the dependence orders.

Suggested Citation

  • K. Mosler, 2003. "Central regions and dependency," Econometrics 0309004, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpem:0309004
    Note: Type of Document - Post Script; pages: 16 ; figures: included. This is a preprint of an article accepted for publication in "Methology and Computing in Applied Probability"

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    References listed on IDEAS

    1. Dall'Aglio, Marco & Scarsini, Marco, 2001. "When Lorenz met Lyapunov," Statistics & Probability Letters, Elsevier, vol. 54(1), pages 101-105, August.
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    More about this item


    Dependence order; generalized correlation; lift zonoid volume; data depth; trimmed regions;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics


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