论文标题
基于双变量藤本型复合物回归，双变量水平和分位曲线
Bivariate vine copula based regression, bivariate level and quantile curves
论文作者
论文摘要
单变量分位数的统计分析是一个发达的研究主题。但是，需要研究多元分位数。我们使用基于葡萄藤的双变量回归模型的水平曲线构建双变量（条件）分位数。葡萄藤是图形的理论模型，该模型通过一系列链接的树确定，该模型允许对边缘分布和依赖性结构进行单独的建模。我们介绍了一种新型的图形结构模型（由树序列给出），专为预测回归设置中的两个响应的对称处理而设计。我们建立了模型的计算障碍和获得不同条件分布的直接方法。避免了对预测因子的转换或相互作用，截线性或分位数交叉的需求，使用葡萄藤的典型回归短缺。我们说明了基于Copula的双变量曲线的不同copula分布，并展示了如何调整它们以形成有效的分数曲线。我们将我们的方法应用于韩国首尔的天气测量。该数据示例强调了与两个单独的单变量回归或假设有条件的独立性相比，在有条件依赖性的情况下，双变量响应数据集与两个单独的单变量回归相比。
The statistical analysis of univariate quantiles is a well developed research topic. However, there is a need for research in multivariate quantiles. We construct bivariate (conditional) quantiles using the level curves of vine copula based bivariate regression model. Vine copulas 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 computational tractability of the model and a straight forward way of obtaining different conditional distributions. Using vine copulas the typical shortfalls of regression, as the need for transformations or interactions of predictors, collinearity or quantile crossings are avoided. We illustrate the copula based bivariate level curves for different copula distributions and show how they can be adjusted to form valid quantile curves. We apply our approach to weather measurements from Seoul, Korea. This 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.
