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Ranks, copulas, and permutons

Author

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  • R. Grübel

    (Leibniz Universität Hannover)

Abstract

We review a recent development at the interface between discrete mathematics on one hand and probability theory and statistics on the other, specifically the use of Markov chains and their boundary theory in connection with the asymptotics of randomly growing permutations. Permutations connect total orders on a finite set, which leads to the use of a pattern frequencies. This view is closely related to classical concepts of nonparametric statistics. We give several applications and discuss related topics and research areas, in particular the treatment of other combinatorial families, the cycle view of permutations, and an approach via exchangeability.

Suggested Citation

  • R. Grübel, 2024. "Ranks, copulas, and permutons," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(2), pages 155-182, February.
    • Handle: RePEc:spr:metrik:v:87:y:2024:i:2:d:10.1007_s00184-023-00908-2
    DOI: 10.1007/s00184-023-00908-2
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    References listed on IDEAS

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    1. H Shi & M Drton & F Han, 2022. "On the power of Chatterjee’s rank correlation [Adaptive test of independence based on HSIC measures]," Biometrika, Biometrika Trust, vol. 109(2), pages 317-333.
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