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Keywords:
$d$-copulas; fractal copulas; sample $d$-copulas of order $m$
$d$-copulas; fractal copulas; sample $d$-copulas of order $m$
Summary:
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.
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