The Annals of Statistics

On bootstrap accuracy with censored data

Kani Chen and Shaw-Hwa Lo

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Abstract

In survival analysis with censored data, we consider three closely related survival function estimators: the Kaplan-Meier, Nelson and moment estimators. We derive the Edgeworth expansions for these three estimators with Studentization. Edgeworth expansions for the corresponding bootstrap statistics are also given. It is found that the bootstrap approximation is better than the normal approximation for the Studentized Kaplan-Meier and Nelson estimators, but not so for the Studentized moment estimator. With these results, we construct bootstrap-based confidence intervals with better coverage probabilities. We also include some simulations which show strong agreement with our theoretical findings.

Article information

Source
Ann. Statist., Volume 24, Number 2 (1996), 569-595.

Dates
First available in Project Euclid: 24 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1032894453

Digital Object Identifier
doi:10.1214/aos/1032894453

Mathematical Reviews number (MathSciNet)
MR1394976

Zentralblatt MATH identifier
0860.62036

Subjects
Primary: 62G05: Estimation 62E20: Asymptotic distribution theory

Keywords
Kaplan-Meier estimator Nelson estimator moment estimator Greenwood formula Edgeworth expansion

Citation

Chen, Kani; Lo, Shaw-Hwa. On bootstrap accuracy with censored data. Ann. Statist. 24 (1996), no. 2, 569--595. doi:10.1214/aos/1032894453. https://projecteuclid.org/euclid.aos/1032894453


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