BAHADUR REPRESENTATION OF THE KERNEL QUANTILE ESTIMATOR UNDER RANDOM CENSORSHIP

In this paper, a representation due to Major and Rejto for the Kaplan- Meier estimator is applied to establish a Bahadur representation for t he kernel quantile estimator under random censorship. Comparing it wit h the product-limit quantile estimator, the convergence rate of the re mainder term is substantially improved when F(x) is sufficiently smoot h near the true quantile xi(p). As a consequence, a law of the iterate d logarithm is also obtained. (C) 1995 Academic Press, Inc.