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Estimation and Bootstrap with Censored Data in Fixed Design Nonparametric Regression

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Abstract

We study Beran's extension of the Kaplan-Meier estimator for thesituation of right censored observations at fixed covariate values. Thisestimator for the conditional distribution function at a given value of thecovariate involves smoothing with Gasser-Müller weights. We establishan almost sure asymptotic representation which provides a key tool forobtaining central limit results. To avoid complicated estimation ofasymptotic bias and variance parameters, we propose a resampling methodwhich takes the covariate information into account. An asymptoticrepresentation for the bootstrapped estimator is proved and the strongconsistency of the bootstrap approximation to the conditional distributionfunction is obtained.

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Authors and Affiliations

  1. Department of Mathematics, Limburgs Universitair Centrum, Universitaire Campus, B-3590, Diepenbeek, Belgium

    Ingrid Van Keilegom

Authors
  1. Ingrid Van Keilegom
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  2. Noël Veraverbeke
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Van Keilegom, I., Veraverbeke, N. Estimation and Bootstrap with Censored Data in Fixed Design Nonparametric Regression. Annals of the Institute of Statistical Mathematics 49, 467–491 (1997). https://doi.org/10.1023/A:1003166728321

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