Copulas are multivariate distributions whose margins are uniform on the unit interval. They provide a handy tool for the modeling of dependence between variables whose distributions are heterogeneous or involve covariates. This allows in particular for the construction of very versatile dependence models that go beyond the multivariate Gaussian distribution. These models are now extensively used in various applications, e.g., in hydrology, finance, insurance, and risk management.

This course will provide an introduction to statistical inference for copula models. 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 rankbased methods. Diagnostic tools for the detection of dependence and copula selection will also be presented. The methodology is mainly based on the empirical copula process, whose asymptotic behavior will be treated in detail. Throughout, implementation of the inferential tools in the R project of statistical computing will be shown and illustrated on data from hydrology, finance, and insurance.

Students will acquire a good understanding of theoretical and practical aspects of  univariate EVT. Moreover, they will be able to analyze data with EVT.

at least 80% of the units

Classroom teaching; project and group work

The course assessment will be based on project work and on an oral presentation of the project.

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