Abstract
Since Buckley-James estimator can’t always find the only solution and don’t have asymptotically properties. Lai and Ying (1991) introduced a slight modification of the Buckley-James estimators to get around the difficulties and showed that the modified Buckley-James estimator is consistent and asymptotically normal. When the hazards function goes up and down along the time scale, we find the phenomenon local confounding exist between the hazard function h(.) and the covariates x in the modified Buckley James estimating equation. In order to reduce the local confounding effect, we propose the empirical process approach (EPA) based on an empirical process constructed from modified Buckley James estimating equation by varying its truncating time point, and use EPA to improve the estimation.