arXiv subjects

Fabian Spanhel

Publications and source records attributed to Fabian Spanhel.

4 recordsLinked to original sources

arXiv2022

Testing the simplifying assumption in high-dimensional vine copulas

Testing the simplifying assumption in high-dimensional vine copulas is a difficult task. Tests must be based on estimated observations and check 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 high-dimensional 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 dimensionality 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. An application of the test to four real data sets is provided.

stat.ME↗

arXiv2017

The partial vine copula: A dependence measure and approximation based on the simplifying assumption

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, step-wise 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.

stat.ME↗

arXiv2016

Estimating Non-Simplified Vine Copulas Using Penalized Splines

Vine copulas (or pair-copula constructions) have become an important tool for high-dimensional dependence modeling. Typically, so called simplified vine copula models are estimated where bivariate conditional copulas are approximated by bivariate unconditional copulas. We present the first non-parametric estimator of a non-simplified vine copula that allows for varying conditional copulas using penalized hierarchical B-splines. Throughout the vine copula, we test for the simplifying assumption in each edge, establishing a data-driven non-simplified vine copula estimator. To overcome the curse of dimensionality, we approximate conditional copulas with more than one conditioning argument by a conditional copula with the first principal component as conditioning argument. An extensive simulation study is conducted, showing a substantial improvement in the out-of-sample Kullback-Leibler divergence if the null hypothesis of a simplified vine copula can be rejected. We apply our method to the famous uranium data and present a classification of an eye state data set, demonstrating the potential benefit that can be achieved when conditional copulas are modeled.

stat.ME↗

arXiv2015

The partial copula: Properties and associated dependence measures

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.

stat.ME↗