A nonparametric symmetry test for absolutely continuous bivariate copulas

Erdely, Arturo; González-Barrios, José M.

doi:10.1007/s10260-010-0147-7

Cited by 4 publications

(3 citation statements)

References 19 publications

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“…Therefore, a powerful nonparametric test of independence à la Deheuvels based on a Cramér-von Mises statistic [8] has been applied, see Table 13.2 for p-values, clearly rejecting independence for both the total sample and subsample 1, not rejecting independence for subsample 2, but with some doubts about rejecting independence in case of subsample 3, since there is no rule to decide if 0.1274 is a sufficiently low p-value to reject the null hypothesis. Fortunately, a nonparametric symmetry test [6] has been helpful for taking a final decision on subsample 3: by rejecting symmetry we have to reject independence. In terms of choosing a parametric copula, strong evidence against symmetry is challenging since there is not such a huge catalog of parametric asymmetric copulas as there is indeed for the symmetric case.…”

Section: Discussionmentioning

confidence: 99%

“…13.1 and 13.2), eventhough there was not strong evidence against the symmetry of the underlying copula [6], it was not possible to find a single known parametric family of copulas that could avoid being rejected by a goodness-of-fit-test (see Table 13.5), and an analogous situation for the marginal distributions. One way of tackling such situation is by a totally nonparametric approach, using Bernstein copula [15,16] and Bernstein marginals [12], but paying the price of a noisy regression (see Fig.…”

Section: Final Remarksmentioning

confidence: 93%

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Nonparametric and Semiparametric Bivariate Modeling of Petrophysical Porosity-Permeability Dependence from Well Log Data

Erdely

Díaz-Viera

2010

Copula Theory and Its Applications

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Assessment of rock formation permeability is a complicated and challenging problem that plays a key role in oil reservoir modeling, production forecast, and the optimal exploitation management. Generally, permeability evaluation is performed using porosity-permeability relationships obtained by integrated analysis of various petrophysical measurements taken from cores and wireline well logs. Dependence relationships between pairs of petrophysical variables, such as permeability and porosity, are usually nonlinear and complex, and therefore those statistical tools that rely on assumptions of linearity and/or normality and/or existence of moments are commonly not suitable in this case. But even expecting a single copula family to be able to model a complex bivariate dependency seems to be still too restrictive, at least for the petrophysical variables under consideration in this work. Therefore, we explore the use of the Bernstein copula, and we also look for an appropriate partition of the data into subsets for which the dependence strucure was simpler to model, and then a conditional gluing copula technique is applied to build the bivariate joint distribution for the whole data set.

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Section: Discussionmentioning

confidence: 99%

Section: Final Remarksmentioning

confidence: 93%

Nonparametric and Semiparametric Bivariate Modeling of Petrophysical Porosity-Permeability Dependence from Well Log Data

Erdely

Díaz-Viera

2010

Copula Theory and Its Applications

Self Cite

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“…As a consequence, many tests of parametric and nonparametric symmetry tests are implemented. As a revealing example, we refer to [6] and the important paper of A. Erdely and J. M. Gonzàlez-Barrios [11] and in another and close context [13]. We mention also the attempt of dependence coefficient symmetrization as initiated by Cifarelli et al [7].…”

Section: Asymmetric Copulasmentioning

confidence: 99%

A Functional Treatment of Asymmetric Copulas A. Sani and L. Karbil

2020

Electronic Journal of Mathematical Analysis and Applications

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The concept of asymmetric copulas is revisited and is made more precise. We give a rigorous topological argument for opportunity to define asymmetry measures defined recently by K.F Siburg [6] through exhibiting at least three ordered classes of copulas according to a suitable equivalence relation. We define a process of ordering subcopulas which makes clearer the degree of asymmetry. As illustration, we treat the asymmetric Cobb-Douglas utility model.

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On approximating dependence function and its derivatives

Tajvidi

2024

Extremes

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Bivariate extreme value distributions can be used to model dependence of observations from random variables in extreme levels. There is no finite dimensional parametric family for these distributions, but they can be characterized by a certain one-dimensional function which is known as Pickands dependence function. In many applications the general approach is to estimate the dependence function with a non-parametric method and then conduct further analysis based on the estimate. Although this approach is flexible in the sense that it does not impose any special structure on the dependence function, its main drawback is that the estimate is not available in a closed form. This paper provides some theoretical results which can be used to find a closed form approximation for an exact or an estimate of a twice differentiable dependence function and its derivatives. We demonstrate the methodology by calculating approximations for symmetric and asymmetric logistic dependence functions and their second derivatives. We show that the theory can be even applied to approximating a non-parametric estimate of dependence function using a convex optimization algorithm. Other discussed applications include a procedure for testing whether an estimate of dependence function can be assumed to be symmetric and estimation of the concordance measures of a bivariate extreme value distribution. Finally, an Australian annual maximum temperature dataset is used to illustrate how the theory can be used to build semi-infinite and compact predictions regions.

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A nonparametric symmetry test for absolutely continuous bivariate copulas

Cited by 4 publications

References 19 publications

Nonparametric and Semiparametric Bivariate Modeling of Petrophysical Porosity-Permeability Dependence from Well Log Data

Nonparametric and Semiparametric Bivariate Modeling of Petrophysical Porosity-Permeability Dependence from Well Log Data

A Functional Treatment of Asymmetric Copulas A. Sani and L. Karbil

On approximating dependence function and its derivatives

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