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On the minimum information checkerboard copula under fixed Kendall’s $$\tau $$ τ

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  • Issey Sukeda

    (The University of Tokyo)

  • Tomonari Sei

    (The University of Tokyo)

Abstract

Copulas have gained widespread popularity as statistical models to represent dependence structures between multiple variables in various applications. The minimum information copula, given a finite number of constraints in advance, emerges as the copula closest to the independent copula when measured in Kullback–Leibler divergence. In prior research, the focus has predominantly been on constraints related to expectations on moments, including Spearman’s $$\rho $$ ρ . This approach allows for obtaining the copula through convex programming. However, the existing framework for minimum information copulas does not encompass non-linear constraints such as Kendall’s $$\tau $$ τ . To address this limitation, we introduce MICK, a novel minimum information copula under fixed Kendall’s $$\tau $$ τ . We first characterize MICK by its local dependence property. Despite being defined as the solution to a non-convex optimization problem, we demonstrate that the uniqueness of this copula is guaranteed when its correlation is sufficiently small.

Suggested Citation

  • Issey Sukeda & Tomonari Sei, 2025. "On the minimum information checkerboard copula under fixed Kendall’s $$\tau $$ τ," Statistical Papers, Springer, vol. 66(1), pages 1-39, January.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:1:d:10.1007_s00362-024-01648-9
    DOI: 10.1007/s00362-024-01648-9
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    References listed on IDEAS

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    1. Butucea, Cristina & Delmas, Jean-François & Dutfoy, Anne & Fischer, Richard, 2015. "Maximum entropy copula with given diagonal section," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 61-81.
    2. Perrone, Elisa & Solus, Liam & Uhler, Caroline, 2019. "Geometry of discrete copulas," Journal of Multivariate Analysis, Elsevier, vol. 172(C), pages 162-179.
    3. Tim Bedford & Kevin Wilson, 2014. "On the construction of minimum information bivariate copula families," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(4), pages 703-723, August.
    4. Dehling, Herold & Vogel, Daniel & Wendler, Martin & Wied, Dominik, 2017. "Testing For Changes In Kendall’S Tau," Econometric Theory, Cambridge University Press, vol. 33(6), pages 1352-1386, December.
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