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. © 2013 Elsevier Inc.
|Original language||English (US)|
|Number of pages||15|
|Journal||Journal of Multivariate Analysis|
|State||Published - Jan 2014|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-CI-016-04
Acknowledgements: Chen's research was partially sponsored by NSF (SES-0838161). Cheng's research was sponsored by NSF (DMS-0906497 and CAREER Award DMS-1151692). Huang's research was partly sponsored by NSF (DMS-0907170, DMS-1007618), and Award Number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST). Zhou's research was partially sponsored by NSF (DMS-0907170). The authors thank the editor, the associate editor, and one referee for insightful comments that led to important improvements in the paper.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.