The Experts below are selected from a list of 38685 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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Using model distances to investigate the Simplifying Assumption, model selection and truncation levels for vine copulas
2017Co-Authors: Matthias Killiches, Claudia CzadoAbstract:Vine copulas are a useful statistical tool to describe the dependence structure between several random variables, especially when the number of variables is very large. When modeling data with vine copulas, one often is confronted with a set of candidate models out of which the best one is supposed to be selected. For example, this may arise in the context of non-simplified vine copulas, truncations of vines and other simplifications regarding pair-copula families or the vine structure. With the help of distance measures we develop a parametric bootstrap based testing procedure to decide between copulas from nested model classes. In addition we use distance measures to select among different candidate models. All commonly used distance measures, e.g. the Kullback-Leibler distance, suffer from the curse of dimensionality due to high-dimensional integrals. As a remedy for this problem, Killiches, Kraus and Czado (2017) propose several modifications of the Kullback-Leibler distance. We apply these distance measures to the above mentioned model selection problems and substantiate their usefulness.
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Using model distances to investigate the Simplifying Assumption, goodness-of-fit and truncation levels for vine copulas
arXiv: Methodology, 2016Co-Authors: Matthias Killiches, Daniel Kraus, Claudia CzadoAbstract:Vine copulas are a useful statistical tool to describe the dependence structure between several random variables, especially when the number of variables is very large. When modeling data with vine copulas, one often is confronted with a set of candidate models out of which the best one is supposed to be selected. For example, this may arise in the context of non-simplified vine copulas, truncations of vines and other simplifications regarding pair-copula families or the vine structure. With the help of distance measures we develop a parametric bootstrap based testing procedure to decide between copulas from nested model classes. In addition we use distance measures to assess the goodness-of-fit of different candidate models. All commonly used distance measures, e.g. the Kullback-Leibler distance, suffer from the curse of dimensionality due to high-dimensional integrals. As a remedy for this problem, Killiches, Kraus and Czado (2016) propose several modifications of the Kullback-Leibler distance. We apply these distance measures to the above mentioned model selection problems and substantiate their usefulness.
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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.
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 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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d vine copula based quantile regression and the Simplifying Assumption for vine copulas
2017Co-Authors: Daniel KrausAbstract:In the first part of this thesis we propose a novel semiparametric approach to perform quantile regression using D-vine copulas, a subclass of the flexible class of vine copula models. Various applications and the extension to discrete data are presented. In the second part the Simplifying Assumption for vine copulas is discussed, focussing on its visual implications and the development of a formal test. Finally, two new tree structure selection methods for vine copulas are developed.
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Using model distances to investigate the Simplifying Assumption, goodness-of-fit and truncation levels for vine copulas
arXiv: Methodology, 2016Co-Authors: Matthias Killiches, Daniel Kraus, Claudia CzadoAbstract:Vine copulas are a useful statistical tool to describe the dependence structure between several random variables, especially when the number of variables is very large. When modeling data with vine copulas, one often is confronted with a set of candidate models out of which the best one is supposed to be selected. For example, this may arise in the context of non-simplified vine copulas, truncations of vines and other simplifications regarding pair-copula families or the vine structure. With the help of distance measures we develop a parametric bootstrap based testing procedure to decide between copulas from nested model classes. In addition we use distance measures to assess the goodness-of-fit of different candidate models. All commonly used distance measures, e.g. the Kullback-Leibler distance, suffer from the curse of dimensionality due to high-dimensional integrals. As a remedy for this problem, Killiches, Kraus and Czado (2016) propose several modifications of the Kullback-Leibler distance. We apply these distance measures to the above mentioned model selection problems and substantiate their usefulness.
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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.
S.c. Wang - One of the best experts on this subject based on the ideXlab platform.
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The strength of friction stir welded and friction stir processed aluminium alloys
Scripta Materialia, 2008Co-Authors: M.j. Starink, A. Deschamps, S.c. WangAbstract:Local strength of friction stir (FS) welds and FS processed aluminium alloys in heat-treatable aluminium alloys is dominated by precipitation hardening. Strengthening due to stored dislocations is generally limited to 40 MPa, and grain size strengthening is generally less than 10 MPa. Local crystallographic texture can cause yield strength variation on the order of 5%. Published models for strengthening of FS welds make a range of Simplifying Assumption which can cause uncertainties in the predictions of up to 50 MPa. Possible improvements are explored.
Ricardo A Lebensohn - One of the best experts on this subject based on the ideXlab platform.
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Factors contributing to plastic strain amplification in slip dominated deformation of magnesium alloys
Modelling and Simulation in Materials Science and Engineering, 2015Co-Authors: C. W. Sinclair, G. Martin, Ricardo A LebensohnAbstract:While plastic strains are never distributed uniformly in polycrystals, it has recently been shown experimentally that the distribution can be extremely heterogeneous in magnesium polycrystals even when the deformation is dominated by slip. Here, we attempt to provide insight into the (macroscopic) factors that contribute to this strain amplification and to explain, from a local perspective, the origins of this strain amplification. To do this, full field VPFFT crystal plasticity simulations have been performed under the Simplifying Assumption that twinning is inoperative. It is shown that the experimentally observed heterogeneity can be reproduced when a sufficiently high anisotropy in slip system strength is assumed. This can be further accentuated by a weakening of the texture.
M.j. Starink - One of the best experts on this subject based on the ideXlab platform.
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The strength of friction stir welded and friction stir processed aluminium alloys
Scripta Materialia, 2008Co-Authors: M.j. Starink, A. Deschamps, S.c. WangAbstract:Local strength of friction stir (FS) welds and FS processed aluminium alloys in heat-treatable aluminium alloys is dominated by precipitation hardening. Strengthening due to stored dislocations is generally limited to 40 MPa, and grain size strengthening is generally less than 10 MPa. Local crystallographic texture can cause yield strength variation on the order of 5%. Published models for strengthening of FS welds make a range of Simplifying Assumption which can cause uncertainties in the predictions of up to 50 MPa. Possible improvements are explored.
