The Experts below are selected from a list of 42066 Experts worldwide ranked by ideXlab platform
Claudia Czado - One of the best experts on this subject based on the ideXlab platform.
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Growing simplified vine Copula trees: improving Dißmann's algorithm
2017Co-Authors: Daniel Kraus, Claudia CzadoAbstract:Vine Copulas are pair-Copula constructions enabling multivariate dependence modeling in terms of bivariate building blocks. One of the main tasks of fitting a vine Copula is the selection of a suitable tree structure. For this the prevalent method is a heuristic called Dismann's algorithm. It sequentially constructs the vine's trees by maximizing dependence at each tree level, where dependence is measured in terms of absolute Kendall's tau. However, the algorithm disregards any implications of the tree structure on the simplifying assumption that is usually made for vine Copulas to keep inference tractable. We develop two new algorithms that select tree structures focused on producing simplified vine Copulas for which the simplifying assumption is violated as little as possible. For this we make use of a recently developed statistical test of the simplifying assumption. In a simulation study we show that our proposed methods outperform the benchmark given by Dismann's algorithm by a great margin. Several real data applications emphasize their practical relevance.
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Growing simplified vine Copula trees: improving Di{\ss}mann's algorithm
arXiv: Methodology, 2017Co-Authors: Daniel Kraus, Claudia CzadoAbstract:Vine Copulas are pair-Copula constructions enabling multivariate dependence modeling in terms of bivariate building blocks. One of the main tasks of fitting a vine Copula is the selection of a suitable tree structure. For this the prevalent method is a heuristic called Di{\ss}mann's algorithm. It sequentially constructs the vine's trees by maximizing dependence at each tree level, where dependence is measured in terms of absolute Kendall's $\tau$. However, the algorithm disregards any implications of the tree structure on the simplifying assumption that is usually made for vine Copulas to keep inference tractable. We develop two new algorithms that select tree structures focused on producing simplified vine Copulas for which the simplifying assumption is violated as little as possible. For this we make use of a recently developed statistical test of the simplifying assumption. In a simulation study we show that our proposed methods outperform the benchmark given by Di{\ss}mann's algorithm by a great margin. Several real data applications emphasize their practical relevance.
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Examination and visualisation of the simplifying assumption for vine Copulas in three dimensions
arXiv: Applications, 2016Co-Authors: Matthias Killiches, Daniel Kraus, Claudia CzadoAbstract:Vine Copulas are a highly flexible class of dependence models, which are based on the decomposition of the density into bivariate building blocks. For applications one usually makes the simplifying assumption that Copulas of conditional distributions are independent of the variables on which they are conditioned. However this assumption has been criticised for being too restrictive. We examine both simplified and non-simplified vine Copulas in three dimensions and investigate conceptual differences. We show and compare contour surfaces of three-dimensional vine Copula models, which prove to be much more informative than the contour lines of the bivariate marginals. Our investigation shows that non-simplified vine Copulas can exhibit arbitrarily irregular shapes, whereas simplified vine Copulas appear to be smooth extrapolations of their bivariate margins to three dimensions. In addition to a variety of constructed examples, we also investigate a three-dimensional subset of the well-known uranium data set and visually detect that a non-simplified vine Copula is necessary to capture its complex dependence structure.
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simplified pair Copula constructions limitations and extensions
Journal of Multivariate Analysis, 2013Co-Authors: Jakob Stober, Claudia CzadoAbstract:So-called pair Copula constructions (PCCs), specifying multivariate distributions only in terms of bivariate building blocks (pair Copulas), constitute a flexible class of dependence models. To keep them tractable for inference and model selection, the simplifying assumption, that Copulas of conditional distributions do not depend on the values of the variables which they are conditioned on, is popular.
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modeling longitudinal data using a pair Copula decomposition of serial dependence
Journal of the American Statistical Association, 2010Co-Authors: Michael S Smith, Carlos Almeida, Claudia CzadoAbstract:Copulas have proven to be very successful tools for the flexible modeling of cross-sectional dependence. In this paper we express the dependence structure of continuous-valued time series data using a sequence of bivariate Copulas. This corresponds to a type of decomposition recently called a “vine” in the graphical models literature, where each Copula is entitled a “pair-Copula.” We propose a Bayesian approach for the estimation of this dependence structure for longitudinal data. Bayesian selection ideas are used to identify any independence pair-Copulas, with the end result being a parsimonious representation of a time-inhomogeneous Markov process of varying order. Estimates are Bayesian model averages over the distribution of the lag structure of the Markov process. Using a simulation study we show that the selection approach is reliable and can improve the estimates of both conditional and unconditional pairwise dependencies substantially. We also show that a vine with selection outperforms a Gaussian...
Taizhong Hu - One of the best experts on this subject based on the ideXlab platform.
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pyvine: The Python Package for Regular Vine Copula Modeling, Sampling and Testing
Communications in Mathematics and Statistics, 2019Co-Authors: Zhenfei Yuan, Taizhong HuAbstract:Regular vine Copula provides rich models for dependence structure modeling. It combines vine structures and families of bivariate Copulas to construct a number of multivariate distributions that can model a wide range dependence patterns with different tail dependence for different pairs. Two special cases of regular vine Copulas, C-vine and D-vine Copulas, have been extensively investigated in the literature. We propose the Python package, pyvine , for modeling, sampling and testing a more generalized regular vine Copula (R-vine for short). R-vine modeling algorithm searches for the R-vine structure which maximizes the vine tree dependence in a sequential way. The maximum likelihood estimation algorithm takes the sequential estimations as initial values and uses L-BFGS-B algorithm for the likelihood value optimization. R-vine sampling algorithm traverses all edges of the vine structure from the last tree in a recursive way and generates the marginal samples on each edge according to some nested conditions. Goodness-of-fit testing algorithm first generates Rosenblatt’s transformed data $${\varvec{E}}$$ E and then tests the hypothesis $$H_0^*: {\varvec{E}} \sim C_{\perp }$$ H 0 ∗ : E ∼ C ⊥ by using Anderson–Darling statistic, where $$C_{\perp }$$ C ⊥ is the independence Copula. Bootstrap method is used to compute an adjusted p -value of the empirical distribution of replications of Anderson–Darling statistic. The computing of related functions of Copulas such as cumulative distribution functions, H-functions and inverse H-functions often meets with the problem of overflow. We solve this problem by reinvestigating the following six families of bivariate Copulas: Normal, Student t , Clayton, Gumbel, Frank and Joe’s Copulas. Approximations of the above related functions of Copulas are given when the overflow occurs in the computation. All these are implemented in a subpackage bvCopula , in which subroutines are written in Fortran and wrapped into Python and, hence, good performance is guaranteed.
Zhenfei Yuan - One of the best experts on this subject based on the ideXlab platform.
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pyvine: The Python Package for Regular Vine Copula Modeling, Sampling and Testing
Communications in Mathematics and Statistics, 2019Co-Authors: Zhenfei Yuan, Taizhong HuAbstract:Regular vine Copula provides rich models for dependence structure modeling. It combines vine structures and families of bivariate Copulas to construct a number of multivariate distributions that can model a wide range dependence patterns with different tail dependence for different pairs. Two special cases of regular vine Copulas, C-vine and D-vine Copulas, have been extensively investigated in the literature. We propose the Python package, pyvine , for modeling, sampling and testing a more generalized regular vine Copula (R-vine for short). R-vine modeling algorithm searches for the R-vine structure which maximizes the vine tree dependence in a sequential way. The maximum likelihood estimation algorithm takes the sequential estimations as initial values and uses L-BFGS-B algorithm for the likelihood value optimization. R-vine sampling algorithm traverses all edges of the vine structure from the last tree in a recursive way and generates the marginal samples on each edge according to some nested conditions. Goodness-of-fit testing algorithm first generates Rosenblatt’s transformed data $${\varvec{E}}$$ E and then tests the hypothesis $$H_0^*: {\varvec{E}} \sim C_{\perp }$$ H 0 ∗ : E ∼ C ⊥ by using Anderson–Darling statistic, where $$C_{\perp }$$ C ⊥ is the independence Copula. Bootstrap method is used to compute an adjusted p -value of the empirical distribution of replications of Anderson–Darling statistic. The computing of related functions of Copulas such as cumulative distribution functions, H-functions and inverse H-functions often meets with the problem of overflow. We solve this problem by reinvestigating the following six families of bivariate Copulas: Normal, Student t , Clayton, Gumbel, Frank and Joe’s Copulas. Approximations of the above related functions of Copulas are given when the overflow occurs in the computation. All these are implemented in a subpackage bvCopula , in which subroutines are written in Fortran and wrapped into Python and, hence, good performance is guaranteed.
Daniel Kraus - One of the best experts on this subject based on the ideXlab platform.
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Growing simplified vine Copula trees: improving Di{\ss}mann's algorithm
arXiv: Methodology, 2017Co-Authors: Daniel Kraus, Claudia CzadoAbstract:Vine Copulas are pair-Copula constructions enabling multivariate dependence modeling in terms of bivariate building blocks. One of the main tasks of fitting a vine Copula is the selection of a suitable tree structure. For this the prevalent method is a heuristic called Di{\ss}mann's algorithm. It sequentially constructs the vine's trees by maximizing dependence at each tree level, where dependence is measured in terms of absolute Kendall's $\tau$. However, the algorithm disregards any implications of the tree structure on the simplifying assumption that is usually made for vine Copulas to keep inference tractable. We develop two new algorithms that select tree structures focused on producing simplified vine Copulas for which the simplifying assumption is violated as little as possible. For this we make use of a recently developed statistical test of the simplifying assumption. In a simulation study we show that our proposed methods outperform the benchmark given by Di{\ss}mann's algorithm by a great margin. Several real data applications emphasize their practical relevance.
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Growing simplified vine Copula trees: improving Dißmann's algorithm
2017Co-Authors: Daniel Kraus, Claudia CzadoAbstract:Vine Copulas are pair-Copula constructions enabling multivariate dependence modeling in terms of bivariate building blocks. One of the main tasks of fitting a vine Copula is the selection of a suitable tree structure. For this the prevalent method is a heuristic called Dismann's algorithm. It sequentially constructs the vine's trees by maximizing dependence at each tree level, where dependence is measured in terms of absolute Kendall's tau. However, the algorithm disregards any implications of the tree structure on the simplifying assumption that is usually made for vine Copulas to keep inference tractable. We develop two new algorithms that select tree structures focused on producing simplified vine Copulas for which the simplifying assumption is violated as little as possible. For this we make use of a recently developed statistical test of the simplifying assumption. In a simulation study we show that our proposed methods outperform the benchmark given by Dismann's algorithm by a great margin. Several real data applications emphasize their practical relevance.
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Examination and visualisation of the simplifying assumption for vine Copulas in three dimensions
arXiv: Applications, 2016Co-Authors: Matthias Killiches, Daniel Kraus, Claudia CzadoAbstract:Vine Copulas are a highly flexible class of dependence models, which are based on the decomposition of the density into bivariate building blocks. For applications one usually makes the simplifying assumption that Copulas of conditional distributions are independent of the variables on which they are conditioned. However this assumption has been criticised for being too restrictive. We examine both simplified and non-simplified vine Copulas in three dimensions and investigate conceptual differences. We show and compare contour surfaces of three-dimensional vine Copula models, which prove to be much more informative than the contour lines of the bivariate marginals. Our investigation shows that non-simplified vine Copulas can exhibit arbitrarily irregular shapes, whereas simplified vine Copulas appear to be smooth extrapolations of their bivariate margins to three dimensions. In addition to a variety of constructed examples, we also investigate a three-dimensional subset of the well-known uranium data set and visually detect that a non-simplified vine Copula is necessary to capture its complex dependence structure.
Malte S Kurz - One of the best experts on this subject based on the ideXlab platform.
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simplified vine Copula models approximations based on the simplifying assumption
arXiv: Methodology, 2015Co-Authors: Fabian Spanhel, Malte S KurzAbstract:In the last decade, simplified vine Copula models (SVCMs), or pair-Copula constructions, have become an important tool in high-dimensional dependence modeling. So far, specification and estimation of SVCMs has been conducted under the simplifying assumption, i.e., all bivariate conditional Copulas of the data generating vine are assumed to be bivariate unconditional Copulas. For the first time, we consider the case when the simplifying assumption does not hold and an SVCM acts as an approximation of a multivariate Copula. Several results concerning optimal simplified vine Copula approximations and their properties are established. Under regularity conditions, step-by-step estimators of pair-Copula constructions converge to the partial vine Copula approximation (PVCA) if the simplifying assumption does not hold. The PVCA can be regarded as a generalization of the partial correlation matrix where partial correlations are replaced by j-th order partial Copulas. We show that the PVCA does not minimize the KL divergence from the true Copula and that the best approximation satisfying the simplifying assumption is given by a vine pseudo-Copula. Moreover, we demonstrate how spurious conditional (in)dependencies may arise in SVCMs.
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The partial vine Copula: A dependence measure and approximation based on the simplifying assumption
arXiv: Methodology, 2015Co-Authors: Fabian Spanhel, Malte S KurzAbstract: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.
