Christian Genest and Johanna G. Nešlehová
Copulas are multivariate distributions whose margins are uniform on the interval (0, 1). They provide a handy tool for modeling the dependence between variables whose distributions are heterogeneous or involve covariates. Due to their flexibility, copula models are quickly gaining popularity in hydrology, finance, and insurance. This course will provide an introduction to statistical inference for copula models and its implementation in the R Project for Statistical Computing. The notion of copula and its role in representing dependence will first be explained. A few classical copula models will then be described, along with their properties. Next, it will be shown how estimation and goodness-of-fit testing can be performed using rank-based methods. Diagnostic tools for the detection of dependence and copula selection will also be presented. The continuous case will be considered in detail; adjustments required for handling discrete variables will be mentioned. Advanced topics will be discussed at the end of the course; these include the modeling of extreme-value dependence and strategies for adapting the copula approach to high-dimensional data. Data from hydrology, finance, and insurance will be used throughout the course for illustration purposes.
Last update: March 15, 2017.