arXiv subjects

Cécile Amblard

Publications and source records attributed to Cécile Amblard.

4 recordsLinked to original sources

arXiv2013

Bivariate copulas defined from matrices

We propose a semiparametric family of copulas based on a set of orthonormal functions and a matrix. This new copula permits to reach values of Spearman's Rho arbitrarily close to one without introducing a singular component. Moreover, it encompasses several extensions of FGM copulas as well as copulas based on partition of unity such as Bernstein or checkerboard copulas. Finally, it is also shown that projection of arbitrary densities of copulas onto tensor product bases can enter our framework.

math.ST↗

arXiv2011

Estimation procedures for a semiparametric family of bivariate copulas

In this paper, we propose simple estimation methods dedicated to a semiparametric family of bivariate copulas. These copulas can be simply estimated through the estimation of their univariate generating function. We take profit of this result to estimate the associated measures of association as well as the high probability regions of the copula. These procedures are illustrated on simulations and on real data.

stat.ME↗

arXiv2011

A new bivariate extension of FGM copulas

We propose a new family of copulas generalizing the Farlie-Gumbel-Morgenstern family and generated by two univariate functions. The main feature of this family is to permit the modeling of high positive dependence. In particular, it is established that the range of the Spearman's Rho is [-3/4,1] and that the upper tail dependence coefficient can reach any value in [0,1]. Necessary and sufficient conditions are given on the generating functions in order to obtain various dependence properties. Some examples of parametric subfamilies are provided.

math.ST↗

arXiv2011

Symmetry and dependence properties within a semiparametric family of bivariate copulas

In this paper, we study a semiparametric family of bivariate copulas. The family is generated by an univariate function, determining the symmetry (radial symmetry, joint symmetry) and dependence property (quadrant dependence, total positivity, ...) of the copulas. We provide bounds on different measures of association (such as Kendall's Tau, Spearman's Rho) for this family and several choices of generating functions allowing to reach these bounds.

math.ST↗