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A topological proof of Sklar’s theorem in arbitrary dimensions

Author

Listed:
  • Benth Fred Espen

    (Department of Mathematics, University of Oslo, P. O. Box 1053 Blindern, N-0316 Oslo, Norway)

  • Nunno Giulia Di

    (Department of Mathematics, University of Oslo, P. O. Box 1053 Blindern, N-0316 Oslo, Norway)

  • Schroers Dennis

    (Department of Mathematics, University of Oslo, P. O. Box 1053 Blindern, N-0316 Oslo, Norway)

Abstract

Copulas are appealing tools in multivariate probability theory and statistics. Nevertheless, the transfer of this concept to infinite dimensions entails some nontrivial topological and functional analytic issues, making a deeper theoretical understanding indispensable toward applications. In this short work, we transfer the well-known property of compactness of the set of copulas in finite dimensions to the infinite-dimensional framework. As an application, we prove Sklar’s theorem in infinite dimensions via a topological argument and the notion of inverse systems.

Suggested Citation

  • Benth Fred Espen & Nunno Giulia Di & Schroers Dennis, 2022. "A topological proof of Sklar’s theorem in arbitrary dimensions," Dependence Modeling, De Gruyter, vol. 10(1), pages 22-28, January.
    • Handle: RePEc:vrs:demode:v:10:y:2022:i:1:p:22-28:n:1
    DOI: 10.1515/demo-2022-0103
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    References listed on IDEAS

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    1. Fernández-Sánchez, Juan & Nelsen, Roger B. & Úbeda-Flores, Manuel, 2011. "Multivariate copulas, quasi-copulas and lattices," Statistics & Probability Letters, Elsevier, vol. 81(9), pages 1365-1369, September.
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