Dependence modelling in ultra high dimensions with vine copulas and the Graphical Lasso

Müller, Dominik; Czado, Claudia

doi:10.1016/j.csda.2019.02.007

Cited by 12 publications

(5 citation statements)

References 33 publications

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“…Traditional variable selection methods for regression can also be applied, for example, the forward selection approach. Moreover, recent papers proposed methods for learning sparse vine copula models [21,22], which can be potentially used as a variable selection method for copula regression. Table 4.…”

Section: Resultsmentioning

confidence: 99%

Prediction based on conditional distributions of vine copulas

Chang

Joe

2019

Computational Statistics & Data Analysis

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Vine copulas are a flexible tool for multivariate non-Gaussian distributions. For data from an observational study where the explanatory variables and response variables are measured together, a proposed vine copula regression method uses regular vines and handles mixed continuous and discrete variables. This method can efficiently compute the conditional distribution of the response variable given the explanatory variables. The performance of the proposed method is evaluated on simulated data sets and a real data set. The experiments demonstrate that the vine copula regression method is superior to linear regression in making inferences with conditional heteroscedasticity.

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Section: Resultsmentioning

confidence: 99%

Prediction based on conditional distributions of vine copulas

Chang

Joe

2019

Computational Statistics & Data Analysis

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“…This method is implemented in the vinecopulib library. A separate line of research (Müller & Czado 2018, 2019a exploits connections between vine copulas and Gaussian directed acyclic graphs to find sparsity patterns. A completely different approach is to use dimension reduction techniques before employing a copula model (as in Tagasovska et al 2019).…”

Section: Structure Selection and High-dimensional Modelsmentioning

confidence: 99%

Vine Copula Based Modeling

Czado

Nagler

2022

Annu. Rev. Stat. Appl.

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With the availability of massive multivariate data comes a need to develop flexible multivariate distribution classes. The copula approach allows marginal models to be constructed for each variable separately and joined with a dependence structure characterized by a copula. The class of multivariate copulas was limited for a long time to elliptical (including the Gaussian and t-copula) and Archimedean families (such as Clayton and Gumbel copulas). Both classes are rather restrictive with regard to symmetry and tail dependence properties. The class of vine copulas overcomes these limitations by building a multivariate model using only bivariate building blocks. This gives rise to highly flexible models that still allow for computationally tractable estimation and model selection procedures. These features made vine copula models quite popular among applied researchers in numerous areas of science. This article reviews the basic ideas underlying these models, presents estimation and model selection approaches, and discusses current developments and future directions. Expected final online publication date for the Annual Review of Statistics and Its Application, Volume 9 is March 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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“…The advantage is, of course, the flexibility, but the drawback is that this approach can be computationally unaffordable in terms of estimation, and there is always a possibility of overfitting. Recently, Müller & Czado (2019) proposed a novel three-step approach that overcomes the computational limitation. First, Gaussian methods are applied to split data sets into feasibly small subsets, then parsimonious and flexible vine copulas are applied, and finally, these submodels are reconciled into one joint model.…”

Section: Copulasmentioning

confidence: 99%

“…First, Gaussian methods are applied to split data sets into feasibly small subsets, then parsimonious and flexible vine copulas are applied, and finally, these submodels are reconciled into one joint model. We refer the reader to Müller & Czado (2019) for more details and for an example of the use of vine copulas in high dimensions. A modified Bayesian information criterion (BIC) tailored to sparse vine copula models by Nagler et al (2019) represents another approach for dealing with the computational cost and overfitting in vine copula models for high dimensions.…”

Section: Copulasmentioning

confidence: 99%

Flexible Models for Complex Data with Applications

Ley

Babić

Craens

2021

Annu. Rev. Stat. Appl.

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Probability distributions are the building blocks of statistical modeling and inference. It is therefore of the utmost importance to know which distribution to use in what circumstances, as wrong choices will inevitably entail a biased analysis. In this article, we focus on circumstances involving complex data and describe the most popular flexible models for these settings. We focus on the following complex data: multivariate skew and heavy-tailed data, circular data, toroidal data, and cylindrical data. We illustrate the strength of flexible models on the basis of concrete examples and discuss major applications and challenges. Expected final online publication date for the Annual Review of Statistics and Its Application, Volume 8 is March 8, 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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Dependence modelling in ultra high dimensions with vine copulas and the Graphical Lasso

Cited by 12 publications

References 33 publications

Prediction based on conditional distributions of vine copulas

Prediction based on conditional distributions of vine copulas

Vine Copula Based Modeling

Flexible Models for Complex Data with Applications

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