Geodesic
Sample $d$-copula of order $m$
Kybernetika, Tome 49 (2013) no. 5, pp. 663-691.

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In this paper we analyze the construction of $d$-copulas including the ideas of Cuculescu and Theodorescu [5], Fredricks et al. [15], Mikusiński and Taylor [25] and Trutschnig and Fernández-Sánchez [33]. Some of these methods use iterative procedures to construct copulas with fractal supports. The main part of this paper is given in Section 3, where we introduce the sample $d$-copula of order $m$ with $m≥2$, the central idea is to use the above methodologies to construct a new copula based on a sample. The greatest advantage of the sample $d$-copula is the fact that it is already an approximating $d$-copula and that it is easily obtained. We will see that these new copulas provide a nice way to study multivariate data with an approximating copula which is simpler than the empirical multivariate copula, and that the empirical copula is the restriction to a grid of a sample $d$-copula of order $n$. These sample $d$-copulas can be used to make statistical inference about the distribution of the data, as shown in Section 3.
Classification : 60A10, 60E05, 62E10, 62F05
Keywords: $d$-copulas; fractal copulas; sample $d$-copulas of order $m$ 
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     author = {Gonz\'alez-Barrios, Jos\'e M. and Hern\'andez-Cedillo, Mar{\'\i}a M.},
     title = {Sample $d$-copula of order $m$},
     journal = {Kybernetika},
     pages = {663--691},
     publisher = {mathdoc},
     volume = {49},
     number = {5},
     year = {2013},
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     zbl = {06239460},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2013__49_5_a0/}
}
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González-Barrios, José M.; Hernández-Cedillo, María M. Sample $d$-copula of order $m$. Kybernetika, Tome 49 (2013) no. 5, pp. 663-691. http://geodesic.mathdoc.fr/item/KYB_2013__49_5_a0/