Big data application require the need to understand dependencies among the variables. While the most prominent multivariate distribution in statistics is the normal distribution, it has many short comings. First of all it does not allow for tail dependence, it accommodates only symmetric dependence patterns and requires that all marginal distributions are normal. In contrast a copula approach lets you model the dependence structure completely independent of the choice of marginal distributions. The class of multivariate copulas can be considerably extended using a pair copula construction leading to the so called vine distributions. I will introduce this construction, show estimation and model selection methods and illustrate their usefulness in applications.  In particular I will show case their use in constructing quantile regression models. 

References:

Aas, K., Czado, C., Frigessi, A., & Bakken, H. (2009). Pair-copula constructions of multiple dependence. Insurance: Mathematics and economics, 44(2), 182-198.

Bedford, T., & Cooke, R. M. (2002). Vines: A new graphical model for dependent random variables. Annals of Statistics, 1031-1068.

Joe, H. (2014). Dependence modeling with copulas. CRC Press.

Kraus, D., & Czado, C. (2017). D-vine copula based quantile regression. Computational Statistics & Data Analysis, 110, 1-18.

Websites:

vine-copula.org

en.wikipedia.org/wiki/Vine_copula

Einladung von Prof. Thorsten Dickhaus