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On a class of norms generated by nonnegative integrable distributions

Author

Listed:
  • Falk Michael

    (Institute of Mathematics, University of Würzburg, Würzburg, Germany)

  • Stupfler Gilles

    (School of Mathematical Sciences, University of Nottingham, Nottingham, UK)

Abstract

We show that any distribution function on ℝd with nonnegative, nonzero and integrable marginal distributions can be characterized by a norm on ℝd+1, called F-norm. We characterize the set of F-norms and prove that pointwise convergence of a sequence of F-norms to an F-norm is equivalent to convergence of the pertaining distribution functions in the Wasserstein metric. On the statistical side, an F-norm can easily be estimated by an empirical F-norm, whose consistency and weak convergence we establish.

Suggested Citation

  • Falk Michael & Stupfler Gilles, 2019. "On a class of norms generated by nonnegative integrable distributions," Dependence Modeling, De Gruyter, vol. 7(1), pages 259-278, January.
    • Handle: RePEc:vrs:demode:v:7:y:2019:i:1:p:259-278:n:14
    DOI: 10.1515/demo-2019-0014
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    References listed on IDEAS

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    1. Falk, Michael & Stupfler, Gilles, 2017. "An offspring of multivariate extreme value theory: The max-characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 85-95.
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