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Deheuvels (1981a) described a decomposition of the empirical copula process into a finite number of asymptotically mutually independent sub-processes whose joint limiting distribution is tractable under the hypothesis that a multivariate distribution is equal to the product of its margins. It is proved here that this result can be extended to the serial… (More)

This paper presents an introduction to inference for copula models, based on rank methods. By working out in detail a small, fictitious numerical example, the writers exhibit the various steps involved in investigating the dependence between two random variables and in modeling it using copulas. Simple graphical tools and numerical techniques are presented… (More)

- CHRISTIAN GENEST
- 2006

The tail behavior of sums of dependent risks was considered by Wüthrich (2003) and by Alink et al. (2004, 2005) in the case where the variables are exchangeable and connected through an Archimedean copula model. It is shown here how their result can be extended to a broader class of dependence structures using multivariate extreme-value theory. An explicit… (More)

- CHRISTIAN GENEST
- 2005

When a decision maker chooses to form his/her own probability distribution by combining the opinions of a number of experts, it is sometimes recommended that he/she should do so in such a way as to preserve any form of expert agreement regarding the independence of the events of interest. In this paper, we argue against this recommendation. We show that for… (More)

- Elif F. Acar, Christian Genest, Johanna Neslehová
- J. Multivariate Analysis
- 2012

Any multivariate density can be decomposed through successive conditionings into basic building blocks involving only pairs of variables. The various ways in which this can be done are called regular vines; C-vines and D-vines are prime examples of such structures. A pair-copula construction (PCC) is a modelling strategy in which conditional and… (More)

- Christian Genest, Johan Segers
- J. Multivariate Analysis
- 2010

Wavelet analysis is used to construct a rank-based estimator of a copula density. The procedure, which can be easily implemented with ready-to-use wavelet packages, is based on an algorithm that handles boundary effects automatically. The resulting estimator provides a nonparametric benchmark for the selection of a parametric copula family. From a… (More)

Deheuvels [J. Multivariate Anal. 11 (1981) 102–113] and Genest and Rémillard [Test 13 (2004) 335–369] have shown that powerful rank tests of multivariate independence can be based on combinations of asymptotically independent Cramér–von Mises statistics derived from a Möbius decomposition of the empirical copula process. A result on the large-sample… (More)

A new class of bivariate distributions is introduced and studied, which encompasses Archimedean copulas and extreme value distributions as special cases. Its dependence structure is described, its maximum and minimum attractors are determined, and an algorithm is given for generating observations from any member of this class. It is also shown how it is… (More)

This article proposes new tests of randomness for innovations in a large class of time series models. These tests are based on functionals of empirical processes constructed from either the model residuals or their associated ranks. The asymptotic behavior of these processes is determined under the null hypothesis of randomness. The limiting distributions… (More)