Copula directed acyclic graphs

Pircalabelu, Eugen; Claeskens, Gerda; Gijbels, Irène

doi:10.1007/s11222-015-9599-9

Cited by 11 publications

(2 citation statements)

References 41 publications

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“…There are ample of areas where such constructions are used. An example of this is in the construction of graphs, see for example Pircalabelu et al (2017). The main challenge in such an approach in the context of asymmetric multivariate distributions lies again in providing theoretical support for statistical inference, in a unified manner, irrespectively of the specific lower dimensional asymmetric marginals and/or copula used.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Flexible asymmetric multivariate distributions based on two-piece univariate distributions

2022

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Classical symmetric distributions like the Gaussian are widely used. However, in reality data often display a lack of symmetry. Multiple distributions have been developed to specifically cope with asymmetric data. These can be grouped under the name "skewed distributions". In this paper we present a broad family of flexible multivariate skewed distributions for which statistical inference is a feasible task. The studied family of multivariate skewed distributions is derived by taking affine combinations of independent univariate distributions. These univariate distributions are members of a flexible family of asymmetric distributions and are an important basis for achieving statistical inference. Besides basic properties of the proposed distributions, also statistical inference based on a maximum likelihood approach is presented. We show that under some mild conditions, weak consistency and asymptotic normality of the maximum likelihood estimators hold. These results are backed up by a simulation study which confirms the developed theoretical results and some data examples to illustrate practical applicability.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Flexible asymmetric multivariate distributions based on two-piece univariate distributions

2022

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“…Over the past decade, vine copulas have been used in a variety of applied work, including finance, hydrology, meteorology, biostatistics, machine learning, geology and wind energy; see, e.g., Soto et al (2012), Fan and Patton (2014), Hao and Singh (2015) and Valizadeh et al (2015). Pircalabelu et al (2015) incorporated vine copulas into Bayesian network to deal with continuous variables, while Panagiotelis et al (2012) studied the problem of applying vine copulas to discrete multivariate data. We refer the reader to Joe (2014) for a comprehensive review on vine copulas and related topics.…”

Section: Introductionmentioning

confidence: 99%

Vine copula approximation: a generic method for coping with conditional dependence

Zhang

Bedford

2017

Stat Comput

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Pair-copula constructions (or vine copulas) are structured, in the layout of vines, with bivariate copulas and conditional bivariate copulas. The main contribution of the current work is an approach to the long-standing problem: how to cope with the dependence structure between the two conditioned variables indicated by an edge, acknowledging that the dependence structure changes with the values of the conditioning variables. The changeable dependence problem, though recognized as crucial in the field of multivariate modelling, remains widely unexplored due to its inherent complication and hence is the motivation of the current work. Rather than resorting to traditional parametric or nonparametric methods, we proceed from an innovative viewpoint: approximating a conditional copula, to any required degree of approximation, by utilizing a family of basis functions. We fully incorporate the impact of the conditioning variables on the functional form of a conditional copula by employing local learning methods. The attractions and dilemmas of the pair-copula approximating technique are revealed via simulated data, and its practical importance is evidenced via a real data set.

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Copulae: An overview and recent developments

Größer

Okhrin

2021

WIREs Computational Stats

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Over the decades that have passed since they were introduced, copulae still remain a very powerful tool for modeling and estimating multivariate distributions. This work gives an overview of copula theory and it also summarizes the latest results. This article recalls the basic definition, the most important cases of bivariate copulae, and it then proceeds to a sketch of how multivariate copulae are developed both from bivariate copulae and from scratch. Regarding higher dimensions, the focus is on hierarchical Archimedean, vine, and factor copulae, which are the most often used and most flexible ways to introduce copulae to multivariate distributions. We also provide an overview of how copulae can be used in various fields of data science, including recent results. These fields include but are not limited to time series and machine learning. Finally, we describe estimation and testing methods for copulae in general, their application to the presented copula structures, and we give some specific testing and estimation procedures for those specific copulae.

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Copula directed acyclic graphs

Cited by 11 publications

References 41 publications

Flexible asymmetric multivariate distributions based on two-piece univariate distributions

Flexible asymmetric multivariate distributions based on two-piece univariate distributions

Vine copula approximation: a generic method for coping with conditional dependence

Copulae: An overview and recent developments

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