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Title: Bivariate vine based quantile regression Authors:  Marija Tepegjozova - Technical University Munich (Germany) [presenting]
Claudia Czado - Technische Universitaet Muenchen (Germany)
Abstract: The statistical analysis of univariate quantiles is a well developed and researched topic. However, there is a profound need for research in multivariate quantiles. We tackle the topic of bivariate quantiles and bivariate quantile regression using vine copulas. They are graph theoretical models composed of a sequence of linked trees, which allow for separate modeling of marginal distributions and the dependence structure in the data. We introduce a novel graph structure model or tree sequence specifically designed for a symmetric treatment of two responses in a regression setting. We assure the computational tractability of the model and a straightforward way of obtaining different conditional distributions. Using vine copulas the typical shortfalls of regression, as the need for transformations or interactions of covariates, collinearity or quantile crossings are avoided. We show a proof of concept by illustrating the copula-based bivariate quantiles for different copula distributions and by applying our model in a simulation study. Further, a data example emphasizes the benefits of bivariate modeling in contrast to two separate regressions for the two-response data set.