Asymptotic equivalence between two empirical mean residual life processes

There are two mean residual life estimates for right censored data. One is based on the Kaplan-Meier estimate, the other, based on the Susarla-Van Ryzin estimate for survival function. In this paper, we define the empirical mean residual life process for right censored data and show that the two empirical mean residual life processes based on the Kaplan-Meier and Susarla-Van Ryzin estimates are asymptotically equivalent uniformly on an interval under some conditions. Also we discuss the case which the asymptotic equivalence might fail.