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Estimating non-simplified vine copulas using penalized splines. (English) Zbl 1384.62170
Summary: 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 nonparametric 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.

##### MSC:
 62H05 Characterization and structure theory for multivariate probability distributions; copulas 62G07 Density estimation
##### Software:
KernSmooth; ks; pacotest; SemiPar; VineCopula
Full Text:
##### References:
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