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June 1997 On the rate of uniform convergence of the product-limit estimator: strong and weak laws
Kani Chen, Shaw-Hwa Lo
Ann. Statist. 25(3): 1050-1087 (June 1997). DOI: 10.1214/aos/1069362738

Abstract

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.

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Kani Chen. Shaw-Hwa Lo. "On the rate of uniform convergence of the product-limit estimator: strong and weak laws." Ann. Statist. 25 (3) 1050 - 1087, June 1997. https://doi.org/10.1214/aos/1069362738

Information

Published: June 1997
First available in Project Euclid: 20 November 2003

zbMATH: 0880.62056
MathSciNet: MR1447741
Digital Object Identifier: 10.1214/aos/1069362738

Subjects:
Primary: 62E20, 62G30

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.25 • No. 3 • June 1997
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