A Model Selection Test For Bivariate Failure-Time Data

In this paper, we address two important issues in semiparametric survival model selection for censored data generated by the Archimedean copula family: method of estimating the parametric copulas and data reuse. We demonstrate that for selection among candidate copula models that might all be misspecified, estimators of the parametric copulas based on minimizing the selection criterion function may be preferred to other estimators. To handle the issue of data reuse, we put model selection in the context of hypothesis testing and propose a simple test for model selection from a finite number of parametric copulas. Results from a simulation study and two empirical illustrations confirm our theoretical findings.We thank the editor Peter Phillips, three anonymous referees, and Hal White for their comments, which greatly improved the paper. An earlier version of this paper was presented at the 2005 World Congress Meetings of the Econometric Society, the 2005 Joint Statistical Meetings, the University of Waterloo, and the University of Western Ontario. Chen acknowledges support from the National Science Foundation and the C.V. Starr Center at NYU. Fan acknowledges support from the National Science Foundation. We thank Demian Pouzo for excellent research assistance on the numerical work in this paper and Weijing Wang for providing us with the Fortran code for computing the bivariate Kaplan–Meier estimator of Dabrowska (1988).