Simplified vine copulas (SVCs), or pair-copula constructions, have become an important tool in high-dimensional dependence modeling. So far, specification and estimation of SVCs has been conducted under the simplifying assumption, i.e., all bivariate conditional copulas of the vine are assumed to be bivariate unconditional copulas. We introduce the partial vine copula (PVC) which provides a new multivariate dependence measure and which plays a major role in the approximation of multivariate distributions by SVCs. The PVC is a particular SVC where to any edge a j-th order partial copula is assigned and constitutes a multivariate analogue of the bivariate partial copula.We investigate to what extent the PVC describes the dependence structure of the underlying copula. We show that the PVC does not minimize the Kullback-Leibler divergence from the true copula and that the best approximation satisfying the simplifying assumption is given by a vine pseudo-copula. However, under regularity conditions, stepwise estimators of pair-copula constructions converge to the PVC irrespective of whether the simplifying assumption holds or not. Moreover, we elucidate why the PVC is the best feasible SVC approximation in practice.

Testing the simplifying assumption in high-dimensional vine copulas is a difficult task because tests must be based on estimated observations and amount to checking constraints on high-dimensional distributions.So far, corresponding tests have been limited to single conditional copulas with a low-dimensional set of conditioning variables. We propose a novel testing procedure that is computationally feasible for highdimensional data sets and that exhibits a power that decreases only slightly with the dimension. By discretizing the support of the conditioning variables and incorporating a penalty in the test statistic, we mitigate the curse of dimensions by looking for the possibly strongest deviation from the simplifying assumption. The use of a decision tree renders the test computationally feasible for large dimensions. We derive the asymptotic distribution of the test and analyze its finite sample performance in an extensive simulation study. The utility of the test is demonstrated by its application to 10 data sets with up to 49 dimensions.

The partial correlation coefficient is a commonly used measure to assess the conditional dependence between two random variables. We provide a thorough explanation of the partial copula, which is a natural generalization of the partial correlation coefficient, and investigate several of its properties. In addition, properties of some associated partial dependence measures are examined.

The R package DoubleML implements the double/debiased machine learning framework of . It provides functionalities to estimate parameters in causal models based on machine learning methods. The double machine learning framework consist of three key ingredients: Neyman orthogonality, high-quality machine learning estimation and sample splitting. Estimation of nuisance components can be performed by various state-of-the-art machine learning methods that are available in the mlr3 ecosystem. DoubleML makes it possible to perform inference in a variety of causal models, including partially linear and interactive regression models and their extensions to instrumental variable estimation. The object-oriented implementation of DoubleML enables a high flexibility for the model specification and makes it easily extendable. This paper serves as an introduction to the double machine learning framework and the R package DoubleML. In reproducible code examples with simulated and real data sets, we demonstrate how DoubleML users can perform valid inference based on machine learning methods.

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