标题： 由低维Copula表示的多变量Copula 显示英文标题

标题： Multivariate Copula Expressed by Lower Dimensional Copulas

摘要： 高阶多元概率分布的建模是一个在许多领域中出现的困难问题。 Copula方法是为此目的的一个好选择，但维度灾难仍然存在问题。 在本文中，我们给出一个定理，该定理基于变量之间的条件独立性，仅使用一些低维Copula来表达一个多元Copula。 一般来说，使用这个定理构建一个多元Copula非常困难，这是由于必须满足的一致性性质。 为此，我们引入了样本导出的Copula，并证明涉及的随机变量之间的依赖性仅取决于这个Copula和划分。 通过使用样本导出的Copula，可以成功应用该定理，以利用其某些边缘来构建一个多元离散Copula。 显示英文摘要

摘要： Modeling of high order multivariate probability distribution is a difficult problem which occurs in many fields. Copula approach is a good choice for this purpose, but the curse of dimensionality still remains a problem. In this paper we give a theorem which expresses a multivariate copula by using only some lower dimensional ones based on the conditional independences between the variables. In general the construction of a multivariate copula using this theorem is quite difficult, due the consistency properties which have to be fulfilled. For this purpose we introduce the sample derivated copula, and prove that the dependence between the random variables involved depends just on this copula and on the partition. By using the sample derivated copula the theorem can be successfully applied, in order to to construct a multivariate discrete copula by using some of its marginals.