Bahadur Representation of the Kernel Quantile Estimator under Random Censorship

In this paper, a representation due to Major and Rejtö for the Kaplan-Meier estimator is applied to establish a Bahadur representation for the kernel quantile estimator under random censorship. Comparing it with the product-limit quantile estimator, the convergence rate of the remainder term is substantially improved when F(x) is sufficiently smooth near the true quantile ξp. As a consequence, a law of the iterated logarithm is also obtained.