Quantile regression is a field with steadily growing importance in statistical modeling. It is a complementary method to linear regression, since computing a range of conditional quantile functions provides a more accurate modelling of the stochastic relationship among variables, especially in the tails. We introduce a non-restrictive and highly flexible nonparametric quantile regression approach based on C- and D-vine copulas. Vine copulas allow for separate modeling of marginal distributions and the dependence structure in the data, and can be expressed through a graph theoretical model given by a sequence of trees. This way we obtain a quantile regression model, that overcomes typical issues of quantile regression such as quantile crossings or collinearity, the need for transformations and interactions of variables. Our approach incorporates a two-step ahead ordering of variables, by maximizing the conditional log-likelihood of the tree sequence, while taking into account the next two tree levels. Further, we show that the nonparametric conditional quantile estimator is consistent. The performance of the proposed methods is evaluated in both low- and high-dimensional settings using simulated and real world data. The results support the superior prediction ability of the proposed models.
翻译:量化回归是一个领域,在统计模型中具有越来越重要的意义。它是线性回归的一种补充方法,因为计算一系列有条件的量化函数可以更准确地模拟变量之间的随机关系,特别是在尾巴中。我们采用了基于C-和D-vine copulas的不限制和高度灵活的非对等量化回归方法。 Vine Conulas允许在数据中分别建模边际分布和依赖性结构,并且可以通过树序列给出的图形理论模型来表达。这样,我们获得一个量化回归模型,克服了四分位回归的典型问题,如四分位交叉点或对等,变异点对变异和相互作用的需要。我们的方法包括了两个步骤,先于变量的排序,即最大限度地实现树序列的有条件的对数相似性,同时考虑下两个树级。此外,我们显示非对等质定性的量化估测算仪是一致的。拟议方法的性能在低度和高度模型中,使用模拟和真实世界的预测结果对高度模型进行评估。