The present contribution derives an explicit expression for (a version of) every uni- and multi-variate conditional distribution (i.e., Markov kernel) of Archimedean copulas and uses this representation to generalize a recently established result, saying that in the class of multivariate Archimedean copulas standard uniform convergence implies weak convergence of almost all univariate Markov kernels, to arbitrary multivariate Markov kernels. Moreover, we prove that an Archimedean copula is singular if, and only if, almost all uni- and multivariate Markov kernels are singular. These results are then applied to conditional Archimedean copulas which are reintroduced largely from a Markov kernel perspective and it is shown that convergence, singularity and conditional increasingness carry over from Archimedean copulas to their conditional copulas. As consequence the surprising fact is established that estimating (the generator of) an Archimedean copula directly yields an estimator of (the generator of) its conditional copula. Building upon that, we sketch the use and estimation of a conditional version of a recently introduced dependence measure as alternative to well-known conditional versions of association measures in order to study the dependence behaviour of Archimedean models when fixing covariate values.

翻译：目前的贡献明确体现了(一个版本)Archimeedean coupulas的每个单项和多项有条件分布(即Markov 内核),并用这一表述来概括最近形成的结果,指出在多变的Archimeedean conulas标准统一趋同类别中,几乎所有的单项和多变的Markov 内核都难以融合到任意的多变的Markov内核。此外,我们证明,如果而且只有几乎所有的单项和多变的Markov内核都是奇特的,而且只有几乎所有的单项和多变的马尔科夫内核核是奇特的。这些结果随后被应用于主要从Markov内核角度重新引入的有条件的Archimeede coula 。 这表明,几乎所有单项和有条件的内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内或内核内核内核内核内核内核内核内核内核内核内核内核内或内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内或内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核内核