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September, 1987 A Note on the Uniform Consistency of the Kaplan-Meier Estimator
Jia-Gang Wang
Ann. Statist. 15(3): 1313-1316 (September, 1987). DOI: 10.1214/aos/1176350507

Abstract

Let $\{X_n, n \geq 1\}$ be i.i.d with $P(X_i \leq u) = F(u)$ and $\{U_n, n \geq 1\}$ be i.i.d. with $P(U_i \leq u) = G(u). \hat{F}_n(t)$ is the Kaplan-Meier estimator based on the censored data $(\tilde{X}_i = X_i \wedge U_i, \delta_i = 1_{(X_i \leq U_i)}, 1 \leq i \leq n)$. In this note, it is shown that for $T_n = \max_{1 \leq i \leq n} \tilde{X}_i$, $\mathrm{pr}-\lim_{n \rightarrow \infty} \sup_{t \leq T_n} |\hat{F}_n(t) - F(t)| = 0.$ Hence, the largest interval on which the Kaplan-Meier estimator is uniformly consistent is found.

Citation

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Jia-Gang Wang. "A Note on the Uniform Consistency of the Kaplan-Meier Estimator." Ann. Statist. 15 (3) 1313 - 1316, September, 1987. https://doi.org/10.1214/aos/1176350507

Information

Published: September, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0631.62043
MathSciNet: MR902260
Digital Object Identifier: 10.1214/aos/1176350507

Subjects:
Primary: 62G05
Secondary: 62N05, 62P10

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 3 • September, 1987
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