Theoretical Study of Some Angle Parameter Trigonometric Copulas

Chesneau, Christophe

doi:10.3390/modelling3010010

Cited by 8 publications

(6 citation statements)

References 22 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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“…For the purpose of this paper, the copula defined in Equation ( 6) is called the ratio-sine (RS) copula. It belongs to the family of trigonometric copulas, which have gained a lot of attention these last few years (see, for instance, [10,12,13,28]). They can be used to uncover dependencies hidden in variables based on circular data (see [28]).…”

Section: Presentationmentioning

confidence: 99%

“…As a result, many authors have devised novel strategies for producing copulas with unique forms and manageable dependence properties. See [10][11][12][13][14][15][16][17][18][19][20][21], among others. In particular, the contemporary works of [14,17] have attracted our attention.…”

Section: Introductionmentioning

confidence: 99%

Theoretical Advancements on a Few New Dependence Models Based on Copulas with an Original Ratio Form

Chesneau

2023

Modelling

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Copulas are well-known tools for describing the relationship between two or more quantitative variables. They have recently received a lot of attention, owing to the variable dependence complexity that appears in heterogeneous modern problems. In this paper, we offer five new copulas based on a common original ratio form. All of them are defined with a single tuning parameter, and all reduce to the independence copula when this parameter is equal to zero. Wide admissible domains for this parameter are established, and the mathematical developments primarily rely on non-trivial limits, two-dimensional differentiations, suitable factorizations, and mathematical inequalities. The corresponding functions and characteristics of the proposed copulas are looked at in some important details. In particular, as common features, it is shown that they are diagonally symmetric, but not Archimedean, not radially symmetric, and without tail dependence. The theory is illustrated with numerical tables and graphics. A final part discusses the multi-dimensional variation of our original ratio form. The contributions are primarily theoretical, but they provide the framework for cutting-edge dependence models that have potential applications across a wide range of fields. Some established two-dimensional inequalities may be of interest beyond the purposes of this paper.

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“…Copulas are popular in statistical analyses for bivariate models involving competing risks [20][21][22][23][24][25][32][33][34]. There exist a number of copulas [31], and new copulas keep emerging [35,36]. Copulas are applied to a variety of fields, including reliability [37], ecology [38], meta-analysis [39,40], and econometrics [41].…”

Section: Copula Model For Competing Risksmentioning

confidence: 99%

Likelihood Inference for Copula Models Based on Left-Truncated and Competing Risks Data from Field Studies

Michimae

Emura

2022

Mathematics

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Survival and reliability analyses deal with incomplete failure time data, such as censored and truncated data. Recently, the classical left-truncation scheme was generalized to analyze “field data”, defined as samples collected within a fixed period. However, existing competing risks models dealing with left-truncated field data are not flexible enough. We propose copula-based competing risks models for latent failure times, permitting a flexible parametric form. We formulate maximum likelihood estimation methods under the Weibull, lognormal, and gamma distributions for the latent failure times. We conduct simulations to check the performance of the proposed methods. We finally give a real data example. We provide the R code to reproduce the simulations and data analysis results.

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Theoretical Study of Some Angle Parameter Trigonometric Copulas

Cited by 8 publications

References 22 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

Theoretical Advancements on a Few New Dependence Models Based on Copulas with an Original Ratio Form

Likelihood Inference for Copula Models Based on Left-Truncated and Competing Risks Data from Field Studies

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