Open Access
March, 1991 Estimating a Distribution Function with Truncated and Censored Data
Tze Leung Lai, Zhiliang Ying
Ann. Statist. 19(1): 417-442 (March, 1991). DOI: 10.1214/aos/1176347991


A minor modification of the product-limit estimator is proposed for estimating a distribution function (not necessarily continuous) when the data are subject to either truncation or censoring, or to both, by independent but not necessarily identically distributed truncation-censoring variables. Making use of martingale integral representations and empirical process theory, uniform strong consistency of the estimator is established and weak convergence results are proved for the entire observable range of the function. Numerical results are also given to illustrate the usefulness of the modification, particularly in the context of truncated data.


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Tze Leung Lai. Zhiliang Ying. "Estimating a Distribution Function with Truncated and Censored Data." Ann. Statist. 19 (1) 417 - 442, March, 1991.


Published: March, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0741.62037
MathSciNet: MR1091860
Digital Object Identifier: 10.1214/aos/1176347991

Primary: 62E20
Secondary: 60F05 , 62G05

Keywords: Censoring , empirical process , Martingales , product-limit estimator , stochastic integral , strong consistency , truncated data , weak convergence

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 1 • March, 1991
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