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Efficient estimation of semiparametric copula models for bivariate survival data

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
    7. 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.
    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.
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