Flexible pair-copula estimation in D-vines using bivariate penalized splines

Kauermann, Göran; Schellhase, Christian

doi:10.1007/s11222-013-9421-5

Cited by 24 publications

(35 citation statements)

References 39 publications

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“…Note that the form of the copula density cė 1ė2 |D e (·) (namely the dependence structure between Fė 1 |D e (Xė 1 | X X X e = x e ) and Fė 2 |D e (Xė 2 | X X X e = x e )) can be highly influenced by the value of X X X e . The dependence of the form of cė 1ė2 |D e (·) on X X X e is always intentionally ignored in the community of vine copula, due to certain practical concerns such as computational load and the curse of dimensionality (see, e.g., Kauermann and Schellhase 2014).…”

Section: Vine Copula and Relative Information 21 Vine Copulamentioning

confidence: 99%

“…For this issue, more intensive numerical study is needed. To select the optimal (number of) basis functions, an alternative approach is the regularization method: imposing an appropriate penalty on the log-likelihood [see, e.g., Kauermann and Schellhase (2014)]. However, in terms of the set { 6 p u p (1 − u) 6− p 6 q w q (1 − w) 6−q : 0 ≤ p, q ≤ 6}, the penalized log-likelihood function will have no less than 49 unknown parameters.…”

Section: τ=07mentioning

confidence: 99%

“…Again, they employed the simplifying assumption. Likewise, by adopting the simplifying assumption, Kauermann and Schellhase (2014) approximated conditional bivariate copulas by tensor product of a family of basis functions. So and Yeung (2014) assumed that certain dependence measures, e.g., rank correlation, change with time yet not with conditioning variables.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Vine Copula and Relative Information 21 Vine Copulamentioning

confidence: 99%

Section: τ=07mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Zhang

Bedford

2017

Stat Comput

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“…To remedy this issue, several nonparametric approaches have been proposed: Kauermann and Schellhase (2014) use penalized Bernstein polynomials and Bsplines, Nagler and Czado (2016) use kernel estimators, and Scheffer and Weiß (2016) use a non-penalized Bernstein estimator. A related contribution of Haff and Segers (2015) introduces the empirical pair-copula as an extension of the empirical copula, but does not aim at estimation of the vine copula density which is the focus of this article.…”

Section: Introductionmentioning

confidence: 99%

“…Although our primary goal is to survey and compare existing methods, we extend the estimators proposed by Kauermann and Schellhase (2014), Scheffer and Weiß (2016), and Nagler and Czado (2016) in several ways:…”

Section: Introductionmentioning

confidence: 99%

Nonparametric estimation of simplified vine copula models: comparison of methods

Nagler

Schellhase

Czado

2017

Dependence Modeling

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In the last decade, simplified vine copula models have been an active area of research. They build a high dimensional probability density from the product of marginals densities and bivariate copula densities. Besides parametric models, several approaches to nonparametric estimation of vine copulas have been proposed. In this article, we extend these approaches and compare them in an extensive simulation study and a real data application. We identify several factors driving the relative performance of the estimators. The most important one is the strength of dependence. No method was found to be uniformly better than all others. Overall, the kernel estimators performed best, but do worse than penalized B-spline estimators when there is weak dependence and no tail dependence.

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Simulation of potential evapotranspiration values based on vine copula

Khashei-Siuki

Shahidi

Ramezani

et al. 2021

Meteorological Applications

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Vine copula had a great impact on the study and analysis of dependence structures in various sciences. In multivariate analyses with dimensions of more than two variables, it is associated with computational complexities that solve vine copulas and these problems. In this study, in order to provide an approach to simulate potential evapotranspiration based on meteorological parameters in Birjand meteorological station from different family copulas including Rvine, independent R-vine, Gaussian, independent Gaussian, C-vine, C-vine independent, D-vine and D-vine independent were used. In this regard, vine copula simulation and conditional density were used. In pair correlation analysis of the studied variables using Kendall's tau statistic, dependence structure confirmed the studied parameters. The results showed a minimum correlation of À0.32 and a maximum of 0.77. The results of Akaike's information criteria (AIC), Bayesian information criteria (BIC) and LogLike statistics in evaluating the performance of vine copula dependency structure introduced the C-vine copula as the superior copula for analysing the pair dependence of the studied variables. By introducing the superior dependency structure and internal copulas, the tree sequence of the pair of values under study was obtained. Pair of simulated values was performed using vine copula. Comparison of Kendall's tau values in both simulation and observation modes showed that Kendall's tau values were close to each other in both modes and were approximately similar. The simulation results of vine copula potential evapotranspiration values and precipitation, temperature and relative humidity values showed 92% efficiency. The efficiency of C-vine copula in dependence analysis and simulation of potential evapotranspiration (PET) values is very high, which shows the ability of vine family copulas in multivariate analysis.

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Flexible pair-copula estimation in D-vines using bivariate penalized splines

Cited by 24 publications

References 39 publications

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

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

Nonparametric estimation of simplified vine copula models: comparison of methods

Simulation of potential evapotranspiration values based on vine copula

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