A class of multivariate copulas based on products of bivariate copulas

Abstract

International audienceCopulas are a useful tool to model multivariate distributions. While there exist various families of bivariate copulas, much fewer has been done when the dimension is higher. In this paper we propose a class of multivariate copulas based on products of transformed bivariate copulas. No constraints on the parameters refrain the applicability of the proposed class. Furthermore the analytical forms of the copulas within this class allow to naturally associate a graphical structure which helps to visualize the dependencies and to compute the likelihood efficiently even in high dimension. Numerical experiments are conducted both on simulated and real data thanks to a dedicated R package

A streaming algorithm for bivariate empirical copulas

“…This paper adapts the aforementioned Greenwald and Khanna algorithm (Greenwald and Khanna, 2001) to construct an alternative bivariate data summary, returning queries to the empirical copula function with guaranteed error bounds. Whilst the paper doesn't directly extend the summary to higher dimensions, one can construct models of dependence for such multidimensional data using sets of pair-wise copulas (Aas et al, 2009;Mazo et al, 2015). Therefore, approximations to such a copula can be found by using the -accurate bivariate copula functions considered here.…”

Characterizations of bivariate conic, extreme value, and Archimax copulas

“…As an interesting topic for further research in the directions of the construction and characterization of bivariate copulas as realized in this paper, one can consider the approach to construct n-ary copulas (with n > ) proposed and studied in [36] by functions f , f , . .…”

Multivariate Composite Copulas

“…It is an asymmetric copula presented by Liebscher (2008),0988 and it is also considered by Mazo et al (2015) and Durante and Sempi (2016) recently. Furthermore, for each i = 1, .…”

“…For example, Genest and Rivest (2001), Klement et al (2005), Morillas (2005), Alvoni et al (2009), Durante et al (2010), and Valdez and Xiao (2011) applied a distortion function to copulas for constructing new copulas. Xie et al (2019) transformed a given copula C with two distortion functions, Liebscher (2008) and Mazo et al (2015) applied a series of distortion functions to multiple initial copulas for constructing a family of asymmetric copulas, and Lin et al (2018) applied the stochastic distortion to obtain new copulas with financial background. Based on a straightforward "pairwise max" rule, Zhao and Zhang (2018) utilized power functions to two existing copulas and presented the max-copula.…”