Abstract: We propose a general index model for survival data, that generalizes many commonly used semiparametric survival models and belongs to the framework of dimension reduction. Using a combination of a geometric approach in semiparametrics and a martingale treatment in survival data analysis, we devise estimation procedures that are feasible and do not require covariate-independent censoring, as assumed in many dimension-reduction methods for censored survival data. We establish the root-n consistency and asymptotic normality of the proposed estimators and derive the most efficient estimator in this class for the general index model. Numerical experiments demonstrate the empirical performance of the proposed estimators, and an application to an AIDS data set further illustrates the usefulness of the work.

Key words and phrases: Dimension reduction, general index model, kernel estimation, semiparametric theory, survival analysis.