The Annals of Statistics
- Ann. Statist.
- Volume 25, Number 3 (1997), 1050-1087.
On the rate of uniform convergence of the product-limit estimator: strong and weak laws
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.
Ann. Statist., Volume 25, Number 3 (1997), 1050-1087.
First available in Project Euclid: 20 November 2003
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Chen, Kani; Lo, Shaw-Hwa. On the rate of uniform convergence of the product-limit estimator: strong and weak laws. Ann. Statist. 25 (1997), no. 3, 1050--1087. doi:10.1214/aos/1069362738. https://projecteuclid.org/euclid.aos/1069362738