The estimation of the treatment effect in the two-sample problem with right censoring is of interest in survival analysis. In this article we consider both the location shift model and the scale change model. We establish the large-sample properties of a generalized Hodges-Lehmann type estimator. The strong consistency is established under the minimal possible conditions. The asymptotic normality is also obtained without imposing any conditions on the censoring mechanisms. As a by-product, we also establish a result for the oscillation behavior of the Kaplan-Meier process, which extends the Bahadur result for the empirical process to the censored case.
Xiao-Li Meng. Yiannis Bassiakos. Shaw-Hwa Lo. "Large-Sample Properties for a General Estimator of the Treatment Effect in the Two-Sample Problem with Right Censoring." Ann. Statist. 19 (4) 1786 - 1812, December, 1991. https://doi.org/10.1214/aos/1176348371