By approximating the classical product-limit estimator of a distribution function with an average of iid random variables, we derive sufficient and necessary conditions for the rate of (both strong and weak) uniform convergence of the product-limit estimator over the whole line. These findings somehow fill a longstanding gap in the asymptotic theory of survival analysis. The result suggests a natural way of estimating the rate of convergence. We also prove a related conjecture raised by Gill and discuss its application to the construction of a confidence interval for a survival function near the endpoint.
Publié le : 1997-06-14
Classification:
Law of large numbers,
counting process,
martingale inequality,
Kolmogorov zero-one law,
Feller-Chung lemma,
slowly varying function,
stable law,
domain of attraction,
62E20,
62G30
@article{1069362738,
author = {Chen, Kani and Lo, Shaw-Hwa},
title = {On the rate of uniform convergence of the product-limit estimator: strong and weak laws},
journal = {Ann. Statist.},
volume = {25},
number = {6},
year = {1997},
pages = { 1050-1087},
language = {en},
url = {http://dml.mathdoc.fr/item/1069362738}
}
Chen, Kani; Lo, Shaw-Hwa. On the rate of uniform convergence of the product-limit estimator: strong and weak laws. Ann. Statist., Tome 25 (1997) no. 6, pp. 1050-1087. http://gdmltest.u-ga.fr/item/1069362738/