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.
Publié le : 1987-09-14
Classification:
Lorenz curve,
random censorship,
strong approximation,
survival,
total time on test transform,
weak convergence,
60F17,
62E20,
62G05,
62G10
@article{1176350498,
author = {Horvath, Lajos and Yandell, Brian S.},
title = {Convergence Rates for the Bootstrapped Product-Limit Process},
journal = {Ann. Statist.},
volume = {15},
number = {1},
year = {1987},
pages = { 1155-1173},
language = {en},
url = {http://dml.mathdoc.fr/item/1176350498}
}
Horvath, Lajos; Yandell, Brian S. Convergence Rates for the Bootstrapped Product-Limit Process. Ann. Statist., Tome 15 (1987) no. 1, pp. 1155-1173. http://gdmltest.u-ga.fr/item/1176350498/