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Rank-based inference tools for copula regression, with property and casualty insurance applications

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  • Côté, Marie-Pier
  • Genest, Christian
  • Omelka, Marek

Abstract

Rank-based procedures are commonly used for inference in copula models for continuous responses whose behavior does not depend on covariates. This paper describes how these procedures can be adapted to the broader framework in which (possibly non-linear) regression models for the marginal responses are linked by a copula that does not depend on covariates. The validity of many of these techniques can be derived from the asymptotic equivalence between the classical empirical copula process and its analog based on suitable residuals from the marginal models. Moment-based parameter estimation and copula goodness-of-fit tests are shown to remain valid under weak conditions on the marginal error term distributions, even when the residual-based empirical copula process fails to converge weakly. The performance of these procedures is evaluated through simulation in the context of two general insurance applications: micro-level multivariate insurance claims, and dependent loss triangles.

Suggested Citation

  • Côté, Marie-Pier & Genest, Christian & Omelka, Marek, 2019. "Rank-based inference tools for copula regression, with property and casualty insurance applications," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 1-15.
    • Handle: RePEc:eee:insuma:v:89:y:2019:i:c:p:1-15
    DOI: 10.1016/j.insmatheco.2019.08.001
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    1. Abdallah, Anas & Boucher, Jean-Philippe & Cossette, Hélène, 2015. "Modeling Dependence Between Loss Triangles With Hierarchical Archimedean Copulas," ASTIN Bulletin, Cambridge University Press, vol. 45(3), pages 577-599, September.
    2. Csörgo, Miklós & Horváth, Lajos & Shao, Qi-Man, 1993. "Convergence of integrals of uniform empirical and quantile processes," Stochastic Processes and their Applications, Elsevier, vol. 45(2), pages 283-294, April.
    3. Gladys Barriga & Francisco Louzada-Neto & Edwin Ortega & Vicente Cancho, 2010. "A bivariate regression model for matched paired survival data: local influence and residual analysis," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(4), pages 477-495, November.
    4. Peter Xue‐Kun Song, 2000. "Multivariate Dispersion Models Generated From Gaussian Copula," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(2), pages 305-320, June.
    5. Frees, Edward W. & Valdez, Emiliano A., 2008. "Hierarchical Insurance Claims Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1457-1469.
    6. Neumeyer, Natalie & Omelka, Marek & Hudecová, Šárka, 2019. "A copula approach for dependence modeling in multivariate nonparametric time series," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 139-162.
    7. Genest, Christian & Rémillard, Bruno & Beaudoin, David, 2009. "Goodness-of-fit tests for copulas: A review and a power study," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 199-213, April.
    8. Portier, François & Segers, Johan, 2018. "On the weak convergence of the empirical conditional copula under a simplifying assumption," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 160-181.
    9. Edward Frees & Ping Wang, 2005. "Credibility Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 9(2), pages 31-48.
    10. Irène Gijbels & Marek Omelka & Noël Veraverbeke, 2015. "Estimation of a Copula when a Covariate Affects only Marginal Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 1109-1126, December.
    11. Frees, Edward W. (Jed) & Meyers, Glenn & Cummings, A. David, 2010. "Dependent Multi-Peril Ratemaking Models," ASTIN Bulletin, Cambridge University Press, vol. 40(2), pages 699-726, November.
    12. Wenqing He & Jerald F. Lawless, 2005. "Bivariate location–scale models for regression analysis, with applications to lifetime data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 63-78, February.
    13. Edward Frees & Yunjie (Winnie) Sun, 2010. "Household Life Insurance Demand," North American Actuarial Journal, Taylor & Francis Journals, vol. 14(3), pages 338-354.
    14. Hofert, Marius & Mächler, Martin, 2016. "Parallel and Other Simulations in R Made Easy: An End-to-End Study," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 69(i04).
    15. Genest, Christian & Nešlehová, Johanna G. & Rémillard, Bruno, 2017. "Asymptotic behavior of the empirical multilinear copula process under broad conditions," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 82-110.
    16. Portier, Francois & Segers, Johan, 2018. "On the weak convergence of the empirical conditional copula under a simplifying assumption," LIDAM Reprints ISBA 2018012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    17. Shi, Peng & Frees, Edward W., 2011. "Dependent Loss Reserving using Copulas," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 449-486, November.
    18. Frees, Edward W. & Wang, Ping, 2006. "Copula credibility for aggregate loss models," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 360-373, April.
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    2. Einmahl, John & Zhou, C., 2024. "Tail Copula Estimation for Heteroscedastic Extremes," Discussion Paper 2024-003, Tilburg University, Center for Economic Research.
    3. Marek Omelka & Šárka Hudecová & Natalie Neumeyer, 2021. "Maximum pseudo‐likelihood estimation based on estimated residuals in copula semiparametric models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1433-1473, December.
    4. Einmahl, John & Zhou, C., 2024. "Tail Copula Estimation for Heteroscedastic Extremes," Other publications TiSEM 6bcb09c5-8b19-48b8-9320-b, Tilburg University, School of Economics and Management.

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