Bahadur representation of the kernel quantile estimator under random censorship (Q1898403)

A representation due to \textit{P. Major} and \textit{L. Rejtö} [Ann. Stat. 16, No. 3, 1113-1132 (1988; Zbl 0667.62024)] 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 \(\xi_p\). As a consequence, a law of the iterated logarithm is also obtained.