IDEAS home Printed from https://ideas.repec.org/a/vrs/demode/v7y2019i1p292-321n16.html
   My bibliography  Save this article

On kernel-based estimation of conditional Kendall’s tau: finite-distance bounds and asymptotic behavior

Author

Listed:
  • Derumigny Alexis

    (CREST-ENSAE and University of Twente, 5 Drienerlolaan, 7522 NB Enschede, Netherlands)

  • Fermanian Jean-David

    (CREST-ENSAE, 5, avenue Henry Le Chatelier, 91764Palaiseau cedex, France)

Abstract

We study nonparametric estimators of conditional Kendall’s tau, a measure of concordance between two random variables given some covariates. We prove non-asymptotic pointwise and uniform bounds, that hold with high probabilities. We provide “direct proofs” of the consistency and the asymptotic law of conditional Kendall’s tau. A simulation study evaluates the numerical performance of such nonparametric estimators. An application to the dependence between energy consumption and temperature conditionally to calendar days is finally provided.

Suggested Citation

  • Derumigny Alexis & Fermanian Jean-David, 2019. "On kernel-based estimation of conditional Kendall’s tau: finite-distance bounds and asymptotic behavior," Dependence Modeling, De Gruyter, vol. 7(1), pages 292-321, January.
    • Handle: RePEc:vrs:demode:v:7:y:2019:i:1:p:292-321:n:16
    DOI: 10.1515/demo-2019-0016
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/demo-2019-0016
    Download Restriction: no
    File URL: https://libkey.io/10.1515/demo-2019-0016?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
    ---><---

    References listed on IDEAS

    as
    1. Bessec, Marie & Fouquau, Julien, 2008. "The non-linear link between electricity consumption and temperature in Europe: A threshold panel approach," Energy Economics, Elsevier, vol. 30(5), pages 2705-2721, September.
    2. Hobæk Haff, Ingrid & Aas, Kjersti & Frigessi, Arnoldo, 2010. "On the simplified pair-copula construction -- Simply useful or too simplistic?," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1296-1310, May.
    3. Manatunga, Amita K. & Oakes, David, 1996. "A Measure of Association for Bivariate Frailty Distributions," Journal of Multivariate Analysis, Elsevier, vol. 56(1), pages 60-74, January.
    4. 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.
    5. Asimit, Alexandru V. & Gerrard, Russell & Hou, Yanxi & Peng, Liang, 2016. "Tail dependence measure for examining financial extreme co-movements," Journal of Econometrics, Elsevier, vol. 194(2), pages 330-348.
    6. Lajmi Lakhal Chaieb & Louis-Paul Rivest & Belkacem Abdous, 2006. "Estimating survival under a dependent truncation," Biometrika, Biometrika Trust, vol. 93(3), pages 655-669, September.
    7. Moral-Carcedo, Julián & Pérez-García, Julián, 2019. "Time of day effects of temperature and daylight on short term electricity load," Energy, Elsevier, vol. 174(C), pages 169-183.
    8. Acar, Elif F. & Genest, Christian & Nešlehová, Johanna, 2012. "Beyond simplified pair-copula constructions," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 74-90.
    9. Jin-Jian Hsieh & Wei-Cheng Huang, 2015. "Nonparametric estimation and test of conditional Kendall's tau under semi-competing risks data and truncated data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(7), pages 1602-1616, July.
    10. Fermanian, Jean-David & Wegkamp, Marten H., 2012. "Time-dependent copulas," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 19-29.
    11. Lajmi Lakhal & Louis-Paul Rivest & Belkacem Abdous, 2008. "Estimating Survival and Association in a Semicompeting Risks Model," Biometrics, The International Biometric Society, vol. 64(1), pages 180-188, March.
    12. Andrew J. Patton, 2006. "Estimation of multivariate models for time series of possibly different lengths," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(2), pages 147-173, March.
    13. Martin, Emily C. & Betensky, Rebecca A., 2005. "Testing Quasi-Independence of Failure and Truncation Times via Conditional Kendall's Tau," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 484-492, June.
    14. Fermanian, Jean-David & Lopez, Olivier, 2018. "Single-index copulas," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 27-55.
    15. Pardo, Angel & Meneu, Vicente & Valor, Enric, 2002. "Temperature and seasonality influences on Spanish electricity load," Energy Economics, Elsevier, vol. 24(1), pages 55-70, January.
    16. Derumigny, Alexis & Fermanian, Jean-David, 2019. "A classification point-of-view about conditional Kendall’s tau," Computational Statistics & Data Analysis, Elsevier, vol. 135(C), pages 70-94.
    17. 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.
    18. repec:dau:papers:123456789/8180 is not listed on IDEAS
    19. Andrew J. Patton, 2006. "Modelling Asymmetric Exchange Rate Dependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 527-556, May.
    20. Liu, Aiai & Hou, Yanxi & Peng, Liang, 2015. "Interval estimation for a measure of tail dependence," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 294-305.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Alexis Derumigny & Jean-David Fermanian, 2018. "About Kendall's regression," Working Papers 2018-01, Center for Research in Economics and Statistics.
    3. Derumigny, Alexis & Fermanian, Jean-David, 2019. "A classification point-of-view about conditional Kendall’s tau," Computational Statistics & Data Analysis, Elsevier, vol. 135(C), pages 70-94.
    4. Grazian, Clara & Dalla Valle, Luciana & Liseo, Brunero, 2022. "Approximate Bayesian conditional copulas," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    5. Gijbels, Irène & Omelka, Marek & Pešta, Michal & Veraverbeke, Noël, 2017. "Score tests for covariate effects in conditional copulas," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 111-133.
    6. Derumigny, Alexis & Fermanian, Jean-David, 2020. "On Kendall’s regression," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    7. 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.
    8. Gijbels Irène & Matterne Margot, 2021. "Study of partial and average conditional Kendall’s tau," Dependence Modeling, De Gruyter, vol. 9(1), pages 82-120, January.
    9. 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.
    10. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    11. Jean-David Fermanian & Olivier Lopez, 2015. "Single-index copulae," Working Papers 2015-12, Center for Research in Economics and Statistics.
    12. Fermanian, Jean-David & Lopez, Olivier, 2018. "Single-index copulas," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 27-55.
    13. Craiu, V. Radu & Sabeti, Avideh, 2012. "In mixed company: Bayesian inference for bivariate conditional copula models with discrete and continuous outcomes," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 106-120.
    14. Stöber, Jakob & Joe, Harry & Czado, Claudia, 2013. "Simplified pair copula constructions—Limitations and extensions," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 101-118.
    15. Chabouni, Naima & Belarbi, Yacine & Benhassine, Wassim, 2020. "Electricity load dynamics, temperature and seasonality Nexus in Algeria," Energy, Elsevier, vol. 200(C).
    16. Kajal Lahiri & Liu Yang, 2023. "Predicting binary outcomes based on the pair-copula construction," Empirical Economics, Springer, vol. 64(6), pages 3089-3119, June.
    17. Jean-David Fermanian, 2012. "An overview of the goodness-of-fit test problem for copulas," Papers 1211.4416, arXiv.org.
    18. 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.
    19. Levi, Evgeny & Craiu, Radu V., 2018. "Bayesian inference for conditional copulas using Gaussian Process single index models," Computational Statistics & Data Analysis, Elsevier, vol. 122(C), pages 115-134.
    20. Jin Xisong & Lehnert Thorsten, 2018. "Large portfolio risk management and optimal portfolio allocation with dynamic elliptical copulas," Dependence Modeling, De Gruyter, vol. 6(1), pages 19-46, February.

    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:vrs:demode:v:7:y:2019:i:1:p:292-321:n:16. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    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.