Evading the curse of dimensionality in nonparametric density estimation with simplified vine copulas

Nagler, Thomas; Czado, Claudia

doi:10.1016/j.jmva.2016.07.003

Cited by 136 publications

(130 citation statements)

References 41 publications

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“…Note that the curse of dimensionality still apparently remains because conditional marginal cdfs F k|J (·|X J ) are invoked with di erent subsets J of increasing sizes. But this curse can be avoided by calling recursively the non-parametric copulas that have been estimated before (see [30]). …”

Section: Remark 1 the Simplifying Assumption H Does Not Imply That Cmentioning

confidence: 99%

About tests of the “simplifying” assumption for conditional copulas

Derumigny

Fermanian

2017

Dependence Modeling

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Abstract:We discuss the so-called "simplifying assumption" of conditional copulas in a general framework. We introduce several tests of the latter assumption for non-and semiparametric copula models. Some related test procedures based on conditioning subsets instead of point-wise events are proposed. The limiting distributions of such test statistics under the null are approximated by several bootstrap schemes, most of them being new. We prove the validity of a particular semiparametric bootstrap scheme. Some simulations illustrate the relevance of our results.

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Section: Remark 1 the Simplifying Assumption H Does Not Imply That Cmentioning

confidence: 99%

About tests of the “simplifying” assumption for conditional copulas

Derumigny

Fermanian

2017

Dependence Modeling

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“…Either of these issues are often easily addressed by increasing 585 sample sizes or changing hyperparameter settings for the kernel density 586 estimator. Although kernel density estimation in high dimensional spaces 587 remains an open research problem, we have found vine copula kernel density 588 estimation works well for the dimensionality of output measurements we 589 investigate here [23].…”

mentioning

confidence: 86%

“…Each parameter sample is then mapped 302 to an output value, q [i] = q(θ [i] ). The collection of output samples is 303 then fitted using a vine copula kernel density estimator (KDE) [23],Ψ = 304 arg max Ψ p q [1] , . .…”

Section: Implementation Of Cmc 293mentioning

confidence: 99%

A Monte Carlo method to estimate cell population heterogeneity

Lambert

Gavaghan

Tavener

2019

Preprint

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1 Abstract 1Variation is characteristic of all living systems. Laboratory techniques 2 such as flow cytometry can probe individual cells, and, after decades of 3 experimentation, it is clear that even members of genetically identical cell 4 populations can exhibit differences. To understand whether variation is 5 biologically meaningful, it is essential to discern its source. Mathematical 6 models of biological systems are tools that can be used to investigate causes 7 of cell-to-cell variation. From mathematical analysis and simulation of these 8 models, biological hypotheses can be posed and investigated, then parameter 9 inference can determine which of these is compatible with experimental data. 10 Data from laboratory experiments often consist of "snapshots" representing 11 distributions of cellular properties at different points in time, rather than 12 individual cell trajectories. These data are not straightforward to fit using 13 hierarchical Bayesian methods, which require the number of cell population 14 clusters to be chosen a priori. Here, we introduce a computational sampling 15 method named "Contour Monte Carlo" for estimating mathematical model 16 parameters from snapshot distributions, which is straightforward to imple-17 ment and does not require cells be assigned to predefined categories. Our 18 method is appropriate for systems where observed variation is mostly due to 19 variability in cellular processes rather than experimental measurement error, 20 which may be the case for many systems due to continued improvements in 21 resolution of laboratory techniques. In this paper, we apply our method 22 to quantify cellular variation for three biological systems of interest and 23 provide Julia code enabling others to use this method. 24

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“…Additionally several nonparametric methods for the estimation of the pair‐copulas in a vine model have been developed, e.g. kernel density based estimation (Nagler & Czado ), estimation using splines (Kauermann & Schellhase ; Schellhase & Spanhel ) and the empirical copula (Hobæk Haff & Segers ). Furthermore there is a multitude of real data applications, especially in the context of finance (e.g.…”

Section: Vine Copulas and The Simplifying Assumptionmentioning

confidence: 99%

Examination and visualisation of the simplifying assumption for vine copulas in three dimensions

Killiches

Kraus

Czado

2017

Aus NZ J of Statistics

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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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Evading the curse of dimensionality in nonparametric density estimation with simplified vine copulas

Cited by 136 publications

References 41 publications

About tests of the “simplifying” assumption for conditional copulas

About tests of the “simplifying” assumption for conditional copulas

A Monte Carlo method to estimate cell population heterogeneity

Examination and visualisation of the simplifying assumption for vine copulas in three dimensions

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