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Vine copula approximation: a generic method for coping with conditional dependence

机译：葡萄copula逼近：处理条件依赖的通用方法

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Pair-copula constructions (or vine copulas) are structured, in the layout of vines, with bivariate copulas and conditional bivariate copulas. The main contribution of the current work is an approach to the long-standing problem: how to cope with the dependence structure between the two conditioned variables indicated by an edge, acknowledging that the dependence structure changes with the values of the conditioning variables. The changeable dependence problem, though recognized as crucial in the field of multivariate modelling, remains widely unexplored due to its inherent complication and hence is the motivation of the current work. Rather than resorting to traditional parametric or nonparametric methods, we proceed from an innovative viewpoint: approximating a conditional copula, to any required degree of approximation, by utilizing a family of basis functions. We fully incorporate the impact of the conditioning variables on the functional form of a conditional copula by employing local learning methods. The attractions and dilemmas of the pair-copula approximating technique are revealed via simulated data, and its practical importance is evidenced via a real data set.
机译：在葡萄藤的布局中，双对虾构造（或葡萄对虾）具有双变量对虾和有条件的双变量对虾。当前工作的主要贡献是解决了一个长期存在的问题的方法：如何处理边缘指示的两个条件变量之间的依存结构，并确认依赖结构随条件变量的值而变化。尽管可变依赖问题在多元建模领域中被认为是至关重要的，但由于其固有的复杂性，它仍然未被广泛研究，因此是当前工作的动机。我们不是从传统的参数方法或非参数方法中求助，而是从创新的观点出发：通过使用一系列基函数将条件copula逼近到任何所需的逼近程度。通过采用本地学习方法，我们将条件变量对条件语系的功能形式的影响完全纳入其中。通过模拟数据揭示了对对偶逼近技术的吸引力和困境，并通过实际数据集证明了其实际重要性。

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