IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v123y2014icp330-344.html
   My bibliography  Save this article

Efficient estimation of semiparametric copula models for bivariate survival data

Author

Listed:
  • Cheng, Guang
  • Zhou, Lan
  • Chen, Xiaohong
  • Huang, Jianhua Z.

Abstract

A semiparametric copula model for bivariate survival data is characterized by a parametric copula model of dependence and nonparametric models of two marginal survival functions. Efficient estimation for the semiparametric copula model has been recently studied for the complete data case. When the survival data are censored, semiparametric efficient estimation has only been considered for some specific copula models such as the Gaussian copulas. In this paper, we obtain the semiparametric efficiency bound and efficient estimation for general semiparametric copula models for possibly censored data. We construct an approximate maximum likelihood estimator by approximating the log baseline hazard functions with spline functions. We show that our estimates of the copula dependence parameter and the survival functions are asymptotically normal and efficient. Simple consistent covariance estimators are also provided. Numerical results are used to illustrate the finite sample performance of the proposed estimators.

Suggested Citation

  • Cheng, Guang & Zhou, Lan & Chen, Xiaohong & Huang, Jianhua Z., 2014. "Efficient estimation of semiparametric copula models for bivariate survival data," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 330-344.
    • Handle: RePEc:eee:jmvana:v:123:y:2014:i:c:p:330-344
    DOI: 10.1016/j.jmva.2013.10.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X13002157
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2013.10.008?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. Chen, Xiaohong & Fan, Yanqin & Pouzo, Demian & Ying, Zhiliang, 2010. "Estimation and model selection of semiparametric multivariate survival functions under general censorship," Journal of Econometrics, Elsevier, vol. 157(1), pages 129-142, July.
    2. Chen, Xiaohong & Fan, Yanqin & Tsyrennikov, Viktor, 2006. "Efficient Estimation of Semiparametric Multivariate Copula Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1228-1240, September.
    3. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    4. Ying Zhang & Lei Hua & Jian Huang, 2010. "A Spline‐Based Semiparametric Maximum Likelihood Estimation Method for the Cox Model with Interval‐Censored Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 338-354, June.
    5. Nan, Bin & Lin, Xihong & Lisabeth, Lynda D. & Harlow, Sioban D., 2006. "Piecewise Constant Cross-Ratio Estimation for Association of Age at a Marker Event and Age at Menopause," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 65-77, March.
    6. Van Keilegom I. & Hettmansperger T. P., 2002. "Inference on Multivariate M Estimators Based on Bivariate Censored Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 328-336, March.
    7. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
    8. Andreas Wienke & Paul Lichtenstein & Anatoli I. Yashin, 2003. "A Bivariate Frailty Model with a Cure Fraction for Modeling Familial Correlations in Diseases," Biometrics, The International Biometric Society, vol. 59(4), pages 1178-1183, December.
    9. Yi Li & Ross L. Prentice & Xihong Lin, 2008. "Semiparametric maximum likelihood estimation in normal transformation models for bivariate survival data," Biometrika, Biometrika Trust, vol. 95(4), pages 947-960.
    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. Yuan Wu & Christina D. Chambers & Ronghui Xu, 2019. "Semiparametric sieve maximum likelihood estimation under cure model with partly interval censored and left truncated data for application to spontaneous abortion," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(3), pages 507-528, July.

    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. Lawless, Jerald F. & Yilmaz, Yildiz E., 2011. "Comparison of semiparametric maximum likelihood estimation and two-stage semiparametric estimation in copula models," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2446-2455, July.
    2. Patton, Andrew, 2013. "Copula Methods for Forecasting Multivariate Time Series," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 899-960, Elsevier.
    3. Dennis Kristensen, 2009. "Semiparametric Modelling and Estimation: A Selective Overview," CREATES Research Papers 2009-44, Department of Economics and Business Economics, Aarhus University.
    4. Sukjin Han & Sungwon Lee, 2019. "Estimation in a generalization of bivariate probit models with dummy endogenous regressors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(6), pages 994-1015, September.
    5. Chen, Xiaohong & Huang, Zhuo & Yi, Yanping, 2021. "Efficient estimation of multivariate semi-nonparametric GARCH filtered copula models," Journal of Econometrics, Elsevier, vol. 222(1), pages 484-501.
    6. Braekers, Roel & Van Keilegom, Ingrid, 2009. "Flexible modeling based on copulas in nonparametric median regression," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1270-1281, July.
    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. Thomas, Alban & Chakir, Raja, 2020. "Unintended consequences of environmental policies: the case of set-aside and agricultural intensification," TSE Working Papers 20-1066, Toulouse School of Economics (TSE).
    9. Chen, Xiaohong & Fan, Yanqin & Pouzo, Demian & Ying, Zhiliang, 2010. "Estimation and model selection of semiparametric multivariate survival functions under general censorship," Journal of Econometrics, Elsevier, vol. 157(1), pages 129-142, July.
    10. Schwiebert, Jörg, 2012. "Analyzing the Composition of the Female Workforce - A Semiparametric Copula Approach," Hannover Economic Papers (HEP) dp-503, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    11. Daniel Ackerberg & Xiaohong Chen & Jinyong Hahn, 2012. "A Practical Asymptotic Variance Estimator for Two-Step Semiparametric Estimators," The Review of Economics and Statistics, MIT Press, vol. 94(2), pages 481-498, May.
    12. Liebscher, Eckhard, 2008. "Construction of asymmetric multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2234-2250, November.
    13. Xiaohong Chen & Wei Biao Wu Wu & Yanping Yi, 2009. "Efficient estimation of copula-based semiparametric Markov models," CeMMAP working papers CWP06/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    14. Xiaohong Chen & Zhuo Huang & Yanping Yi, 2019. "Efficient Estimation of Multivariate Semi-nonparametric GARCH Filtered Copula Models," Cowles Foundation Discussion Papers 2215, Cowles Foundation for Research in Economics, Yale University.
    15. Lajmi Lakhal-Chaieb & Thierry Duchesne, 2017. "Association measures for bivariate failure times in the presence of a cure fraction," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(4), pages 517-532, October.
    16. Dennis Kristensen, 2009. "Semiparametric modelling and estimation (in Russian)," Quantile, Quantile, issue 7, pages 53-83, September.
    17. Kristensen, Dennis, 2010. "Pseudo-maximum likelihood estimation in two classes of semiparametric diffusion models," Journal of Econometrics, Elsevier, vol. 156(2), pages 239-259, June.
    18. Steven Abrams & Paul Janssen & Jan Swanepoel & Noël Veraverbeke, 2020. "Nonparametric estimation of the cross ratio function," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 771-801, June.
    19. Qian M. Zhou, 2024. "Information matrix equivalence in the presence of censoring: a goodness-of-fit test for semiparametric copula models with multivariate survival data," Statistical Papers, Springer, vol. 65(7), pages 4677-4713, September.
    20. Daniel Ackerberg & Xiaohong Chen & Jinyong Hahn, 2011. "Asymptotic Variance Estimator for Two-Step Semiparametric Estimators," Cowles Foundation Discussion Papers 1803, Cowles Foundation for Research in Economics, Yale University.

    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:jmvana:v:123:y:2014:i:c:p:330-344. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.