Goodness‐of‐fit Procedures for Copula Models Based on the Probability Integral Transformation

Genest, Christian; Quessy, Jean‐François; Rémillard, Bruno

doi:10.1111/j.1467-9469.2006.00470.x

Cited by 357 publications

(265 citation statements)

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“…We then apply the first d − 1 components to build a general goodness-of-fit test for d-dimensional Archimedean copulas. This complements goodness-of-fit tests based on the dth component, the Kendall distribution function, see, e.g., [13,26], or [14]. Our proposed test can be interpreted as an Archimedean analogon to goodness-of-fit tests based on Rosenblatt's transformation for copulas in general as it establishes a link between a sampling algorithm and a goodness-of-fit test.…”

Section: Introductionmentioning

confidence: 96%

“…For reasons why Archimedean copulas are used in practice, see [9] or [19]. Goodness-of-fit techniques for copulas only more recently gained interest, see, e.g., [5,6,8,[11][12][13][14], and references therein. Although usually presented in a ddimensional setting, only some of the publications actually try to apply goodnessof-fit tests in more than two dimensions, including [5,26] up to dimension d = 5 and [4] up to dimension d = 8.…”

Section: Introductionmentioning

confidence: 99%

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Goodness-of-fit Tests for Archimedean Copulas in High Dimensions

Hering

Hofert

2015

Innovations in Quantitative Risk Management

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A goodness-of-fit transformation for Archimedean copulas is presented from which a test can be derived. In a large-scale simulation study it is shown that the test performs well according to the error probability of the first kind and the power under several alternatives, especially in high dimensions where this test is (still) easy to apply. The test is compared to commonly applied tests for Archimedean copulas. However, these are usually numerically demanding (according to precision and runtime), especially when the dimension is large. The transformation underlying the newly proposed test was originally used for sampling random variates from Archimedean copulas. Its correctness is proven under weaker assumptions. It may be interpreted as an analogon to Rosenblatt's transformation which is linked to the conditional distribution method for sampling random variates. Furthermore, the suggested goodness-of-fit test complements a commonly used goodness-of-fit test based on the Kendall distribution function in the sense that it utilizes all other components of the transformation except the Kendall distribution function. Finally, a graphical test based on the proposed transformation is presented.

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Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Goodness-of-fit Tests for Archimedean Copulas in High Dimensions

Hering

Hofert

2015

Innovations in Quantitative Risk Management

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“…Let us note that, in general, (7) is a non-linear least-squares optimization problem and (8), (9) and (10) are linear inequality constraints on the parameter vector θ. It is known that even unconstrained free-knot least-squares splines are virtually impossible to find (see e.g.…”

Section: P Are the So Called Greville Abscissae Defined On Thementioning

confidence: 99%

“…In order to implement this test and find appropriate p values for the test statistics T n , one can apply the following algorithm, suggested by [9] for a related problem.…”

Section: Goodness Of Fit Testingmentioning

confidence: 99%

GeD spline estimation of multivariate Archimedean copulas

Dimitrova¹,

Kaishev²,

Penev

2008

Computational Statistics & Data Analysis

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A new multivariate Archimedean copula estimation method is proposed in a non-parametric setting. The method uses the so called Geometrically Designed splines (GeD splines), recently introduced by Kaishev et al. (2006 a,b) [10] and [11], to represent the cdf of a random variable W θ , obtained through the probability integral transform of an Archimedean copula with parameter θ. Sufficient conditions for the GeD spline estimator to posses the properties of the underlying theoretical cdf, K(θ, t), of W θ , are given. The latter conditions allow for defining a three-step estimation procedure for solving the resulting non-linear regression problem with linear inequality constraints. In the proposed procedure, finding the number and location of the knots and the coefficients of the unconstrained GeD spline estimator and solving the constraint least-squares optimisation problem, are separated. Thus, the resulting spline estimatorK(θ, t) is used to recover the generator and the related Archimedean copula by solving an ordinary differential equation. The proposed method is truly multivariate, it brings about numerical efficiency and as a result can be applied with large volumes of data and for dimensions d ≥ 2, as illustrated by the numerical examples presented.

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“…Simply, the copula is nothing more than a way of creating a joint probability distribution for two or more variables while preserving their marginal distributions [27]. From the definitions of copula, it is much clearer that the copula has proven to be a useful tool in the analysis of dependency structures in statistics [14,27]. Thus, the copula contains all information about the dependence between random variables [15].…”

Section: Introductionmentioning

confidence: 99%

A statistical method for assessing agreement between two methods of heteroscedastic clinical measurements using the copula method

Aravind¹,

Nawarathna²

2017

J Med Stat Inform

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Background: A method comparison study is a topic of considerable interest in health and biomedical-related fields. The use of this study is to compare a new method with a standard established method. There are two typical steps in method comparison studies, namely modeling the data set and using the fitted model to analyze method comparison data. Methods: As a usual practice to model method comparison data, many recommend a mixed-effects model which assumes constant error variance (homoscedasticity) and normality of error terms. However, these assumptions are generally violated in practice. Thus, in this study, our main goal is to propose a copula based model to deal with non-replicated method comparison data. Moreover, a simulation procedure is carried out to validate the proposed model by means of different copula models. Results: Results indicate that the Normal and Gumbel copulas give more accurate results in terms of bias, mean-squared error and coverage probability values of estimators. Further it is confirmed that the accuracy of model increases with the Kendall tau (τ) correlation between methods and the number of observations. Furthermore, the proposed methodology is illustrated by analyzing finger and arm systolic blood pressure data. Besides the Total Deviation Index (TDI) and Concordance Correlation Coefficient (CCC) values are used to check the agreement between the two methods. Conclusion:The proposed model based on the Copula method can be used to model the method comparison data with balanced and unbalanced data designs.

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Goodness‐of‐fit Procedures for Copula Models Based on the Probability Integral Transformation

Cited by 357 publications

References 50 publications

Goodness-of-fit Tests for Archimedean Copulas in High Dimensions

Goodness-of-fit Tests for Archimedean Copulas in High Dimensions

GeD spline estimation of multivariate Archimedean copulas

A statistical method for assessing agreement between two methods of heteroscedastic clinical measurements using the copula method

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