An exact bootstrap approach towards modification of the Harrell–Davis quantile function estimator for censored data

Abstract

A new kernel quantile estimator is proposed for right-censored data, which takes the form of , where w _{j(u, c)} is based on a beta kernel with bandwidth parameter c. The advantage of this estimator is that exact bootstrap methods may be employed to estimate the mean and variance of [Qcirc](u; c). It follows that a novel solution for finding the optimal bandwidth may be obtained through minimization of the exact bootstrap mean squared error (MSE) estimate of [Qcirc](u; c). We prove the large sample consistency of [Qcirc](u; c) for fixed values of c. A Monte Carlo simulation study shows that our estimator is significantly better than the product-limit quantile estimator [Qcirc] _KM(u)=inf{t:[Fcirc] _n (t)≥u}, with respect to various MSE criteria. For general simplicity, setting c=1 leads to an extension of classical Harrell–Davis estimator for censored data and performs well in simulations. The procedure is illustrated by an application to lung cancer survival data.

Keywords:

• bootstrap
• order statistics
• kernel quantile smoothing

Acknowledgements

We wish to thank the Associate Editor and two reviewers for their careful reading of the original manuscript and for their constructive comments, which significantly improved the paper.