Estimation and Bootstrap with Censored Data in Fixed Design Nonparametric Regression
(1997) Annals of the Institute of Statistical Mathematics — Vol. 49, n° 3, p. 467-491 (1997)
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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.
- Affiliations
Limburgs Universitair Centrum
Citations
Van Keilegom, I., & Veraverbeke, N. (1997). Estimation and Bootstrap with Censored Data in Fixed Design Nonparametric Regression. Annals of the Institute of Statistical Mathematics, 49(3), 467-491. https://doi.org/10.1023/A:1003166728321 (Original work published 1997)