The Annals of Statistics

Convergence Rates for the Bootstrapped Product-Limit Process

Lajos Horvath and Brian S. Yandell

Full-text: Open access

Abstract

We establish rates for strong approximations of the bootstrapped product-limit process and the corresponding quantile process. These results are used to show weak convergence of bootstrapped total time on test and Lorenz curve processes to the same limiting Gaussian processes as for the unbootstrapped versions. We develop fully nonparametric confidence bands and tests for these curves and apply these results to prostate cancer. We also present almost sure results for the bootstrapped product-limit estimator.

Article information

Source
Ann. Statist., Volume 15, Number 3 (1987), 1155-1173.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350498

Digital Object Identifier
doi:10.1214/aos/1176350498

Mathematical Reviews number (MathSciNet)
MR902251

Zentralblatt MATH identifier
0637.62014

JSTOR
links.jstor.org

Subjects
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 62E20: Asymptotic distribution theory 62G05: Estimation 62G10: Hypothesis testing

Keywords
Lorenz curve random censorship strong approximation survival total time on test transform weak convergence

Citation

Horvath, Lajos; Yandell, Brian S. Convergence Rates for the Bootstrapped Product-Limit Process. Ann. Statist. 15 (1987), no. 3, 1155--1173. doi:10.1214/aos/1176350498. https://projecteuclid.org/euclid.aos/1176350498


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