The Annals of Statistics

A study of a class of weighted bootstraps for censored data

Lancelot F. James

Full-text: Open access

Abstract

Edgeworth expansions are derived for a class of weighted bootstrap methods for the Kaplan-Meier and Nelson-Aalen estimates using the methods contained in the monograph by Barbe and Bertail. Von Mises representations up to the third order are established for the weighted bootstrap versions of these estimators. It is shown that there exists weights which outperform Efron's bootstrap method in terms of coverage accuracy. Moreover, it is shown that this holds for a particular choice of gamma weights which are very easy to use in practice. The general weighting schemes are also useful in approximating the posterior distribution of a survival function with respect to mixtures of beta-neutral process priors.

Article information

Source
Ann. Statist., Volume 25, Number 4 (1997), 1595-1621.

Dates
First available in Project Euclid: 9 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1031594733

Digital Object Identifier
doi:10.1214/aos/1031594733

Mathematical Reviews number (MathSciNet)
MR1463566

Subjects
Primary: 62G09: Resampling methods
Secondary: 62G20: Asymptotic properties 62G30: Order statistics; empirical distribution functions 60F17: Functional limit theorems; invariance principles

Keywords
Edgeworth expansions bootstrap weighted bootstrap Kaplan-Meier von Mises differentiable functions mixtures of beta-neutral priors and posterior distributions

Citation

James, Lancelot F. A study of a class of weighted bootstraps for censored data. Ann. Statist. 25 (1997), no. 4, 1595--1621. doi:10.1214/aos/1031594733. https://projecteuclid.org/euclid.aos/1031594733


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