Sequential Truncation of R-Vine Copula Mixture Model for High-Dimensional Datasets

Fadhah Amer Alanazi,Fernando Bobillo

doi:10.1155/2021/3214262

Fadhah Amer Alanazi, Fernando Bobillo

Open Access

https://doi.org/10.1155/2021/3214262

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Abstract

Uncovering hidden mixture dependencies among variables has been investigated in the literature using mixture R-vine copula models. They provide considerable flexibility for modeling multivariate data. As the dimensions increase, the number of the model parameters that need to be estimated is increased dramatically, which comes along with massive computational times and efforts. This situation becomes even much more complex and complicated in the regular vine copula mixture models. Incorporating the truncation method with a mixture of regular vine models will reduce the computation difficulty for the mixture-based models. In this paper, the tree-by-tree estimation mixture model is joined with the truncation method to reduce computational time and the number of parameters that need to be estimated in the mixture vine copula models. A simulation study and real data applications illustrated the performance of the method. In addition, the real data applications show the effect of the mixture components on the truncation level.

Highlights

Copula is a statistical tool used to model dependencies’ structures among variables independently from their margins
One main advantage of copula models is that the modelers are able to model the margins independently from the dependency structures, which is captured via the copula function
consistent Akaike information criteria (CAIC) −2 ln L(θ􏽢) + P(ln(N) + 1), where θ􏽢 is the estimation values of the parameters, N is the number of observation of the modeled variables, and P is the number of the model parameters

Summary

Introduction

Copula is a statistical tool used to model dependencies’ structures among variables independently from their margins. Is forms the main strength of the vine copula models as the dependence shapes may vary from one pair of variables to another. One main advantage of copula models is that the modelers are able to model the margins independently from the dependency structures, which is captured via the copula function Another advantage is the ability of copula families to deal with a wide range of dependency forms including non-Gaussian, Gaussian, and heavy tails. Continuing to the last theorem, let e ∈ Ei, e {l, m}, l 􏼈l1, l2􏼉, and m 􏼈m1, m2􏼉 be the edge that joined Cel and Cem. Joe [28] showed that the conditional marginal distribution, FCel|De(xCel|xDe) and FCem|De(xCem|xDe), can be obtained as follows: FCel|De􏼐xCel|xDe􏼑 zCCl|Dl􏼒FCl,l1|Dl􏼒xCl,l1|xDl􏼓, FCl,l2|Dl􏼒xCl,l2|xDl􏼓􏼓 zFCl,l2 |Dl 􏼒xCl,l2 |xDl 􏼓. For the 31-dimensional dataset and for 2 mixture components, one needs to estimate 2790 parameters. is number highly increases with the dimensions and the number of the mixture components. erefore, model reduction is necessary to reduce the model complexity of the mixture PCC models. is can be achieved by only modeling a limited number of vine trees instead of the full models, where the higher-order trees are set to independent copulas (see, [31])

Mixture R-Vine Models and EM Algorithm

Simulation Study

Conclusion