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Title: Bivariate vine copula based quantile regression with applications in climate data analysis 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 research 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 identified by a sequence of linked trees, which allow for separate modelling of marginal distributions and the dependence structure. We introduce a novel graph structure model (given by a tree sequence) specifically designed for a symmetric treatment of two responses in a predictive regression setting. We establish the computational tractability of the model and a straightforward way of obtaining different conditional distributions. Using vine copulas, the typical shortfalls of regression, such as the need for transformations or interactions of predictors, collinearity or quantile crossings, are avoided. We illustrate the copula-based bivariate quantiles for different copula distributions and provide a climate data set example. Further, the data example emphasizes the benefits of the joint bivariate response modelling in contrast to two separate univariate regressions or by assuming conditional independence, for bivariate response data set in the presence of conditional dependence.