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

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  • Dongliang Wang
  • Alan Hutson
  • Daniel Gaile

Abstract

A new kernel quantile estimator is proposed for right-censored data, which takes the form of , where wj(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.

Suggested Citation

  • Dongliang Wang & Alan Hutson & Daniel Gaile, 2010. "An exact bootstrap approach towards modification of the Harrell–Davis quantile function estimator for censored data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(8), pages 1039-1051.
    • Handle: RePEc:taf:gnstxx:v:22:y:2010:i:8:p:1039-1051
    DOI: 10.1080/10485250903524662
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