1. Department of Probability & Statistics, Peking University, Beijing 100871, China 2. Department of Statistics, Nankai University, Tianjin 300071, China 3. Department of Statistics, Renmin University of China, Beijing 100872, China
Abstract:
We study an estimator of the survival function under the random censoring model. Bahadur-type representation of the estimator
is obtained and asymptotic expression for its mean squared errors is given, which leads to the consistency and asymptotic
normality of the estimator. A data-driven local bandwidth selection rule for the estimator is proposed. It is worth noting
that the estimator is consistent at left boundary points, which contrasts with the cases of density and hazard rate estimation.
A Monte Carlo comparison of different estimators is made and it appears that the proposed data-driven estimators have certain
advantages over the common Kaplan-Meier estmator.