On the Hajek projection for truncated and censored data

Abstract

Large sample properties of the product-limit estimators for truncated or censored data are usually achieved via the empirical cumulative hazard function estimators. Hajek projection of the empirical cumulative hazard function estimator is derived for truncated data and expressed for censored data. It turns out that both projections are asymptotically ni-equivalent but not equal to the respective influence curves. Weak convergences of the empirical cumulative hazard processes are deduced accordingly.