IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v52y2013i2p338-351.html
   My bibliography  Save this article

Testing tail monotonicity by constrained copula estimation

Author

Listed:
  • Gijbels, Irène
  • Sznajder, Dominik

Abstract

In this paper the interest is in testing for tail monotonicity dependence structures between two random variables. The main focus in the presentation of the statistical methodology is on left tail decreasingness, but the developed procedures can also be used for testing for other specific tail monotonicity dependence structures. In order to assess the p-values of the test statistic, we resample from a constrained copula estimator. This can be done in a nonparametric or in a parametric way. The main difficulty is the construction of a constrained estimator and the development of a resampling technique. The finite-sample performances of the proposed testing procedures are investigated in a simulation study and illustrations on real data examples are provided.

Suggested Citation

  • Gijbels, Irène & Sznajder, Dominik, 2013. "Testing tail monotonicity by constrained copula estimation," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 338-351.
    • Handle: RePEc:eee:insuma:v:52:y:2013:i:2:p:338-351
    DOI: 10.1016/j.insmatheco.2013.01.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668713000103
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2013.01.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Frahm, Gabriel & Junker, Markus & Schmidt, Rafael, 2005. "Estimating the tail-dependence coefficient: Properties and pitfalls," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 80-100, August.
    2. O. Scaillet, 2004. "Nonparametric Estimation and Sensitivity Analysis of Expected Shortfall," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 115-129, January.
    3. Gijbels, Irène & Veraverbeke, Noël & Omelka, Marel, 2011. "Conditional copulas, association measures and their applications," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1919-1932, May.
    4. Colangelo, Antonio & Scarsini, Marco & Shaked, Moshe, 2006. "Some positive dependence stochastic orders," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 46-78, January.
    5. Colangelo, Antonio, 2008. "A study on LTD and RTI positive dependence orderings," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2222-2229, October.
    6. Mathieu Bargès & Hélène Cossette & Etienne Marceau, 2009. "TVaR-based capital allocation with copulas," Working Papers hal-00431265, HAL.
    7. Colangelo, Antonio & Scarsini, Marco & Shaked, Moshe, 2005. "Some notions of multivariate positive dependence," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 13-26, August.
    8. McNeil, Alexander J., 1997. "Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 117-137, May.
    9. Bargès, Mathieu & Cossette, Hélène & Marceau, Étienne, 2009. "TVaR-based capital allocation with copulas," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 348-361, December.
    10. Noël Veraverbeke & Marek Omelka & Irène Gijbels, 2011. "Estimation of a Conditional Copula and Association Measures," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(4), pages 766-780, December.
    11. Michel Denuit, 2004. "Nonparametric Tests for Positive Quadrant Dependence," Journal of Financial Econometrics, Oxford University Press, vol. 2(3), pages 422-450.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Berghaus, Betina & Bücher, Axel, 2014. "Nonparametric tests for tail monotonicity," Journal of Econometrics, Elsevier, vol. 180(2), pages 117-126.
    2. Genest Christian & Scherer Matthias, 2023. "When copulas and smoothing met: An interview with Irène Gijbels," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-16, January.
    3. Ledwina, Teresa & Wyłupek, Grzegorz, 2014. "Validation of positive quadrant dependence," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 38-47.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cousin, Areski & Di Bernardino, Elena, 2014. "On multivariate extensions of Conditional-Tail-Expectation," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 272-282.
    2. Abbas Mahdavi & Omid Kharazmi & Javier E. Contreras-Reyes, 2022. "On the Contaminated Weighted Exponential Distribution: Applications to Modeling Insurance Claim Data," JRFM, MDPI, vol. 15(11), pages 1-18, October.
    3. Colangelo Antonio, 2005. "Multivariate hazard orderings of discrete random vectors," Economics and Quantitative Methods qf05010, Department of Economics, University of Insubria.
    4. Said Khalil, 2022. "Expectile-based capital allocation," Working Papers hal-03816525, HAL.
    5. Blier-Wong, Christopher & Cossette, Hélène & Marceau, Etienne, 2023. "Risk aggregation with FGM copulas," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 102-120.
    6. Vernic, Raluca, 2018. "On the evaluation of some multivariate compound distributions with Sarmanov’s counting distribution," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 184-193.
    7. Loisel, Stéphane & Trufin, Julien, 2014. "Properties of a risk measure derived from the expected area in red," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 191-199.
    8. Derumigny Alexis & Fermanian Jean-David, 2017. "About tests of the “simplifying” assumption for conditional copulas," Dependence Modeling, De Gruyter, vol. 5(1), pages 154-197, August.
    9. Jonas Meier, 2020. "Multivariate Distribution Regression," Diskussionsschriften dp2023, Universitaet Bern, Departement Volkswirtschaft.
    10. Cheung, Ka Chun & Phillip Yam, Sheung Chi & Yuen, Fei Lung & Zhang, Yiying, 2020. "Concave distortion risk minimizing reinsurance design under adverse selection," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 155-165.
    11. Qi Liu & Chun Li & Valentine Wanga & Bryan E. Shepherd, 2018. "Covariate†adjusted Spearman's rank correlation with probability†scale residuals," Biometrics, The International Biometric Society, vol. 74(2), pages 595-605, June.
    12. Marra, Giampiero & Radice, Rosalba, 2017. "Bivariate copula additive models for location, scale and shape," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 99-113.
    13. Grazian, Clara & Dalla Valle, Luciana & Liseo, Brunero, 2022. "Approximate Bayesian conditional copulas," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    14. Michel Denuit & Yang Lu, 2021. "Wishart‐gamma random effects models with applications to nonlife insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(2), pages 443-481, June.
    15. Gardes, Laurent & Girard, Stéphane, 2015. "Nonparametric estimation of the conditional tail copula," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 1-16.
    16. repec:wyi:journl:002095 is not listed on IDEAS
    17. Catalina Bolancé & Montserrat Guillén & Alemar Padilla, 2015. "Estimación del riesgo mediante el ajuste de cópulas," Working Papers 2015-01, Universitat de Barcelona, UB Riskcenter.
    18. Bianchi, Pascal & Elgui, Kevin & Portier, François, 2023. "Conditional independence testing via weighted partial copulas," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    19. Véronique Maume-Deschamps & Didier Rullière & Khalil Said, 2017. "Impact of Dependence on Some Multivariate Risk Indicators," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 395-427, June.
    20. Areski Cousin & Elena Di Bernadino, 2013. "On Multivariate Extensions of Value-at-Risk," Working Papers hal-00638382, HAL.
    21. Enrique de Amo & María del Rosario Rodríguez-Griñolo & Manuel Úbeda-Flores, 2024. "Directional Dependence Orders of Random Vectors," Mathematics, MDPI, vol. 12(3), pages 1-14, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:52:y:2013:i:2:p:338-351. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.