Smooth Quantile Processes For Right Censored Data

Abstract

The development of an estimator of a quantile function Q(p) is discussed. The smooth nonparametric estimator Qn(p) of a quantile function Q(p) is defined as the solution to Fn(Qn(p)) = p, where Fn is a smooth Kaplan-Meier estimator of an unknown continuous distribution function F(x). The asymptotic properties of the smooth quantile process, n(Qn(p) - Q(p)) , based on right censored lifetimes are studied. The asymptotic properties of the bootstrap quantile process, n(Q n(p) - Q(p)) are also investigated and shown to have the same limiting distribution as the smooth quantile process. The bootstrap method to approximate the sampling distribution of the smooth quantile process is used to construct simultaneous confidence bands for a quantile function and the difference of two quantile functions. A Monte Carlo simulation is conducted to assess the performance of these confidence bands by computing the lengths and coverage probabilities of the bands. The optimum bandwidth is also investigated.