Collaborative Research Team Project #01
Copula Dependence Modeling: Theory and Applications
This project explores the theory and applications of copula dependence modeling, with a focus on dependence in high dimensions.
Research Category: Information Sciences
Region: National
Date: 2014-2017
Why Study Copula Modeling?
Copulas have emerged as a tool for capturing and modeling dependence since the mid-1980s. They’ve played an important role in a range of applications, from finance and genetics to hydrology.
Existing data-driven methods for conditional copula models are suitable only in low-dimensional problems, and easily become impractical as dimension increases. This project aims to tackle computational challenges in high dimensions.
Areas of Exploration
Multivariate Copula Models
Includes investigating dimension-reduction techniques and variable-merging methods, as well as tests to identify conditional independence among groups of variables.
Feature Interpretation
Includes investigating the interpretation of dependence features in high-dimensional data. This challenge requires careful study of numerical and graphical representations.
Solving Global Challenges
Research Team’s Goals
To develop methodology that will enable flexible inference of conditional dependencies in multivariate copula models. This includes semi- and non-parametric strategies.
This research has the potential to impact finance and genetics applications, in Canada and worldwide. To this end, the collaborators include world-class, statistical scientists and prominent industry partners.
Related Events
Workshop: New Horizons in Copula Modeling | December 15-18, 2014 at Centre de Recherches Mathématiques (CRM)
People Behind the Project
Project Team
Louis-Paul Rivest, Team Leader | McGill University
Christian Genest, Team Leader | McGill University
Collaborators
Elif Acar | University of Manitoba
Radu Craiu | University of Toronto
Harry Joe | University of British Columbia
Johanna Nešlehová | McGill University
Jean-François Quessy | Université du Québec à Trois-Rivières
Bruno Rémillard | HEC Montréal
Claudia Czado | Technische Universität München
Anne-Catherine Favre | Laboratoire d’Étude des Transferts en Hydrologie et Environnement
Anne-Laure Fougères | Université Claude Bernard Lyon 1
Marius Hofert | ETH Zürich
Industry partners include the Banque Nationale du Canada, Bank of Montreal and Institut de recherche d’Hydro-Québec.
Relevant Publications
- E. Cormier, C. Genest & J.G. Nešlehová (December 2014). Using B-splines for nonparametric inference on bivariate extreme-value copulas. Extremes, 17 (4), 633-659. DOI: 10.1007/s10687-014-0199-4.
- M.-P. Côté & C. Genest (March 2015). A copula-based risk aggregation model. The Canadian Journal of Statistics, 43 (1), in press. DOI: 10.1002/cjs.11238.
- F. Tounkara & L.-P. Rivest (2015). Mixture regression models for closed population capture-recapture data. Biometrics, 71, 721-730.
- J.-F. Quessy & O. Kortbi (2016). Minimum-distance statistics for the selection of an asymmetric copula in Khoudraji’s class of models. Statistica Sinica, 16, 177-204.
- C. Genest & F. Chebana (2016). Copula modeling in hydrologic frequency analysis. Chapter 30 of Handbook of Applied Hydrology (V.P. Singh, Editor). McGraw-Hill, New York, 10 pp.
- J.-F. Quessy (2016). A general framework for testing homogeneity hypotheses about copulas extracted from a multivariate vector. Electronic Journal of Statistics, 10, 1064-1097.
- H. Joe & P. Sang (2016). Multivariate models for dependent clusters of variables with conditional independence given aggregation variables. Computational Statistics and Data Analysis, 97, 114-132.
- L.-P. Rivest, F. Verret & S. Baillargeon (2016). Unit level small area estimation with copulas. Canadian Journal of Statistics, 44, 397-415.
- J. Garrido, C. Genest & J. Schulz (2016). Generalized linear models for dependent claims frequency and severity. Insurance: Mathematics & Economics, 70, 2015-215.
- M.-P. Côté, C. Genest & A. Abdallah (2016). Rank-based methods for modeling dependence between loss triangles. European Actuarial Journal, 6, 377-408.
- S.A. Aissaoui, C. Genest & M. Mesfioui (2017). A second look at inference for bivariate Skellam distributions. Stat, 6, in press.
- L. Hua & H. Joe (2017). Multivariate dependence modeling based on comonotonic factors. Journal of Multivariate Analysis.
- H. Joe (2017). Dependence properties of conditional distributions of some copula models. Methodology and Computing in Applied Probability, accepted January 2017. For special issue in the memory of Moshe Shaked.
- J.-F. Quessy, L.-P. Rivest & M.-H. Toupin (2016). On the chi-square copula. Journal of Multivariate Analysis, 150, 40-60.
Contributions by other members of the team:
- F. Camirand-Lemyre, T. Bouezmarni & J.-F. Quessy. Estimation of conditional copulas: Revisiting asymptotic results in the i.i.d. case, and extension to serial dependence. Journal of Business and Economic Statistics (submitted).
- L.-P. Rivest, F. Verret & S. Baillargeon (December 2015). Estimation of the parameters in copula models for small areas. SSC Annual Meeting, June 2015. Proceedings of the Survey Methods Section.
- E. Levi & R. Craiu (December 2015). Gaussian process single index models for conditional copulas.
- C. Hasler, R. Craiu & L.-P. Rivest (August 2016). Vine copula models in multiple imputation methods. International Statistical.
- F. Camirand-Lemyre (2016). Multiplier bootstrap methods for conditional distributions. Statistics and Computing.
- I. Kojadinovic, J.-F. Quessy & T. Rohmer (2016). Testing the constancy of Spearman’s rho in multivariate time series.
- E.F. Acar (December 2015). Non-simplified vine copulas.
- C. Geerdens, E.F. Acar & P. Janssen (December 2015). Conditional copula models for right-censored clustered event time data. Biometrics.
- K. Zhao & E.F. Acar (December 2015). Conditional dependence models under covariate measurement error.
- E.F. Acar & C. Czado (2017). Dynamic Vine Copulas for Multivariate Time Series (invited for submission to the Special Issue “Recent developments in copula models” in Econometrics).
- E. Hoque, P. Azimaee & E. F. Acar (2017). Prediction-based model selection for vine copula models.
- A. Nessie & E. F. Acar (2017). Factor copula analysis for multivariate ordinal data: revisiting the polychoric correlation.
Explore More Stories
National Region
Find Related Programs
Copula Dependence Modeling: Theory and Applications is a Collaborative Research Team project. This program tackles complex problems through a three-year research and training agenda.
CANSSI offers approximately $200,000 for this type of project, which requires a team of faculty, postdocs, and students.