Theoretical Contributions to Three Generalized Versions of the Celebioglu–Cuadras Copula

Chesneau, Christophe

doi:10.3390/analytics2010003

Cited by 10 publications

(11 citation statements)

References 21 publications

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“…Furthermore, these Archimedean copulas allow simple formulas to compute the CG estimators [ 52 ]. However, there are a large number of non-Archimedean copulas popular in a variety of applications, such as the FGM copula, Gaussian copula, trigonometric copula, and Celebioglu–Cuadras copula [ 82 , 83 , 84 , 85 , 86 , 87 ]. As the CG estimators have not been considered for these non-Archimedean copulas, it is of great interest to develop computational tools for them.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Sensitivity Analysis for Survival Prognostic Prediction with Gene Selection: A Copula Method for Dependent Censoring

2023

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Prognostic analysis for patient survival often employs gene expressions obtained from high-throughput screening for tumor tissues from patients. When dealing with survival data, a dependent censoring phenomenon arises, and thus the traditional Cox model may not correctly identify the effect of each gene. A copula-based gene selection model can effectively adjust for dependent censoring, yielding a multi-gene predictor for survival prognosis. However, methods to assess the impact of various types of dependent censoring on the multi-gene predictor have not been developed. In this article, we propose a sensitivity analysis method using the copula-graphic estimator under dependent censoring, and implement relevant methods in the R package “compound.Cox”. The purpose of the proposed method is to investigate the sensitivity of the multi-gene predictor to a variety of dependent censoring mechanisms. In order to make the proposed sensitivity analysis practical, we develop a web application. We apply the proposed method and the web application to a lung cancer dataset. We provide a template file so that developers can modify the template to establish their own web applications.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Sensitivity Analysis for Survival Prognostic Prediction with Gene Selection: A Copula Method for Dependent Censoring

2023

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“…As interdisciplinary demand for accurate and robust modeling increases, copulas continue to play a central role in advancing statistical methodologies and improving our understanding of multivariate dependence patterns. Recent studies in this regard include those in [8], [10], [24], [31], [4], [5] and [34].…”

Section: (Ii)mentioning

confidence: 99%

Exploring Two Modified Ali-Mikhail-Haq Copulas and New Bivariate Logistic Distributions

Chesneau

2024

Pan-Amer. J. Math.

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The Ali-Mikhail-Haq copula is a bivariate ratio-type Archimedean copula known for its simplicity and flexibility in modeling moderate negative and positive dependence structures, making it widely used in various fields. However, it is limited to capturing asymmetric dependence features, significant negative correlations, or versatile tail dependence properties. This research paper proposes two modifications of the Ali-Mikhail-Haq copula that overcome these limitations, but at the price of the loss of the positive dependence nature. Contrary to the common approach that focuses on modifying the corresponding generator function, we apply direct functional changes to the Ali-Mikhail-Haq copula. We thus perturb its Archimedean identity. The first copula has the particularity of being non-exchangeable, capable of reaching an interesting level of negative dependence correlations, and possessing flexible tail dependence properties. The second copula offers another modeling option; it is exchangeable like the Ali-Mikhail-Haq copula, but it benefits from a broader range of negative dependence correlations and more adaptable tail dependence properties. For the two proposed copulas, we investigate their main characteristics, including quadrant dependence, copula density function, conditional copulas, couples of value generation, extended variants via standard copula schemes, comprehensive copula orders, and weighted harmonic mean copula transformations. An application on two new bivariate logistic distributions in a two-component system context is given. When possible, numerical and graphical studies are given to strengthen the theory.

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“…The form in Equation ( 1) is general. In particular, it includes the Gumbel-Barnett copula, obtained with θ ∈ [−1, 0] and A(x) = B(x) = log(x) (see [5]), and the Celebioglu-Cuadras copula, which appears by taking θ ∈ [−1, 1] and A(x) = B(x) = 1 − x (see [19][20][21]). Furthermore, in the very special case where θ ∈ [0, 1], and A(x) = 1 − x and B(x) = log(x), we obtain…”

Section: Introductionmentioning

confidence: 99%

Theoretical Validation of New Two-Dimensional One-Variable-Power Copulas

Chesneau

2023

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One of the most effective ways to illustrate the relationship between two quantitative variables is to describe the corresponding two-dimensional copula. This approach is acknowledged as practical, nonredundant, and computationally manageable in the context of data analysis. Modern data, however, contain a wide variety of dependent structures, and the copulas now in use may not provide the best model for all of them. As a result, researchers seek to innovate by building novel copulas with appealing properties that are also based on original methodologies. The foundations are theoretical; for a copula to be validated, it must meet specific requirements, which frequently dictate the constraints that must be placed on the relevant parameters. In this article, we make a contribution to the understudied field of one-variable-power copulas. We first identify the specific assumptions that, in theory, validate copulas of such nature. Some other general copulas and inequalities are discussed. Our general results are illustrated with numerous examples depending on two or three parameters. We also prove that strong connections exist between our assumptions and well-established distributions. To highlight the importance of our findings, we emphasize a particular two-parameter, one-variable-power copula that unifies the definition of some other copulas. We reveal its versatile shapes, related functions, various symmetry, Archimedean nature, geometric invariance, copula ordering, quadrant dependence, tail dependence, correlations, and distribution generation. Numerical tables and graphics are produced to support some of these properties. The estimation of the parameters based on data is discussed. As a complementary contribution, two new, intriguing one-variable-power copulas beyond the considered general form are finally presented and studied.

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Theoretical Contributions to Three Generalized Versions of the Celebioglu–Cuadras Copula

Cited by 10 publications

References 21 publications

Sensitivity Analysis for Survival Prognostic Prediction with Gene Selection: A Copula Method for Dependent Censoring

Sensitivity Analysis for Survival Prognostic Prediction with Gene Selection: A Copula Method for Dependent Censoring

Exploring Two Modified Ali-Mikhail-Haq Copulas and New Bivariate Logistic Distributions

Theoretical Validation of New Two-Dimensional One-Variable-Power Copulas

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