Identifiability conditions for the linear regression model under right censoring

The consistency of various estimators under the semi-parametric linear regression model and the standard right censorship model (SPLRRC model) has been studied under various assumptions since the 1970s. These assumptions are somewhat sufficient conditions for the identifiability of the parameters under the SPLRRC model. Since then, it has been a difficult open problem in survival analysis to find the necessary and sufficient condition for the identifiability of the parameters under the SPLRRC model. The open problem is solved in this paper. It is of interest to investigate whether the common estimators under this model are consistent under the identifiability condition. Under the latter condition, we show that the Buckley-James estimator and quantile regression estimator can be inconsistent and present partial results on the consistency of the semi-parametric maximum likelihood estimator.