The asymptotic behaviour of linear regression M-estimators for censored data

In a Ph.D. dissertation Hillis (1987) proposes a class of M-estimators for the vector of regression coefficients in the linear regression model with the response variable subject to right censoring. As in M-estimation procedures for uncensored data, this class of estimators is a generalization of maximum likelihood estimators. Hillis also discusses the asymptotic behaviour of the proposed estimators for the special case of the location model. In this paper, we investigate the asymptotic behaviour of the estimators for the more general regression model with random covariates. In particular, we show that under suitable regularity conditions the estimators exist almost surely for sufficiently large sample sizes. We also prove that under suitable assumptions the estimators are consistent and have an asymptotic normal distribution.