Introductory Overview Lecture: Multivariate Data Modeling with Copulas — Invited Special Presentation
JSM Partner Societies, Caucus for Women in Statistics
Organizer(s): Christian Léger, Université de Montréal
Chair(s): Bruno Rémillard, HEC Montreal
Regarded as an esoteric concept 30 years ago, copulas and copula models feature today among the most powerful and appealing ways of accounting for dependence in multivariate data. This modeling strategy has found numerous applications in finance, insurance, biostatistics and environmental sciences. This introductory overview lecture, delivered by two active researchers in the area, will describe in simple terms the fundamental principles of this approach and provide concrete illustrations of its use.
In the first part, the notions of copula and copula models will be introduced. The fundamental role of rank-based techniques for inference purposes will be highlighted. Various tools for model construction, fitting and validation will first be presented in the vanilla case of multivariate continuous data without covariates. It will then be seen how extensions can lead, e.g., to powerful tests of independence for sparse contingency tables and new effective ways of analyzing multivariate time series data.
In the second part, selected examples of advanced copula modeling will be discussed. Ways of combining GLMs with copulas will be illustrated. Various strategies for copula modeling of high-dimensional data will also be sketched, with special emphasis on hierarchical dependence structures and sparsity. Finally, techniques for infering a hierarchical dependence structure from data will be outlined. Illustrations will be drawn from the fields of insurance, finance, and hydrology.