Dimension Reduction and Semiparametric Estimation of Survival Models

Abstract

In this paper, we propose a new dimension reduction method by introducing a nominal regression model with the hazard function as the conditional mean, which naturally retrieves information from complete data and censored data as well. Moreover, without requiring the linearity condition, the new method can estimate the entire central subspace consistently and exhaustively. The method also provides an alternative approach for the analysis of censored data assuming neither the link function nor the distribution. Hence, it exhibits superior robustness properties. Numerical studies show that the method can indeed be readily used to efficiently estimate survival models, explore the data structures and identify important variables.