Title: Vine copula regression with mixed discrete and continuous predictors
Authors: Dorota Kurowicka - Delft University of Technology (Netherlands) [presenting]
Abstract: The purpose is to show how vine copulas can be used in regression type models where one wants to find the relationship between dependent variable $Y$ and predictive variables $X=(X_1,...,X_d)$ and see how $Y$ changes for different realizations of the predictive variables. If the relationship between $Y$ and $X$ is linear, the linear regression is a very powerful and efficient for such problem. However, when more complicated relationships between $Y$ and $X$ exist in the data we want to model, it might be beneficial to find conditional distribution of Y given realizations of the predictive variables using vine copulas. This problem has already been discussed in case when $Y$ and $X$ were continuous variables. However, when we allow the variables to be mixed discrete and continuous some difficulties of applying the vine copula regression have to be overcome. The vine copula regression is computationally much more involved than the linear regression but in many cases leads to a better model. We present benefits and challenges of vine copula regression and illustrate its performance on few examples of data sets from different areas of applications.