Consistency of the Modified Semi-Parametric MLE under the Linear Regression Model with Right-Censored Data

Under the right censorship model and under the linear regression model where may not exist, the modified semi-parametric MLE (MSMLE) was proposed by Yu and Wong [17]. The MSMLE of satisfying infinitely often) if is discontinuous, and the simulation study suggests that it is also consistent and efficient under certain regularity conditions. In this paper, we establish the consistency of the MSMLE under the necessary and sufficient condition that is identifiable. Notice that under the latter assumption, the Buckley-James estimator and the median regression estimator can be inconsistent (see Yu and Dong [20]).