Asymptotic theory for non-parametric estimators from doubly censored data

Non-parametric estimators of the cumulative intensity and survival function, making use of all available information when the data are doubly censored, are introduced. The estimators are constructed by using the product limit estimator based on a subset of the data with delayed entry and right censoring as an initial estimate for the E-M algorithm and iterating only once. The estimators are shown to be consistent and to converge weakly (properly normalized) to Gaussian processes. The results of a small simulation study is presented.