The Annals of Statistics

Estimating a Distribution Function with Truncated and Censored Data

Tze Leung Lai and Zhiliang Ying

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 19, Number 1 (1991), 417-442.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347991

Digital Object Identifier
doi:10.1214/aos/1176347991

Mathematical Reviews number (MathSciNet)
MR1091860

Zentralblatt MATH identifier
0741.62037

JSTOR
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62G05: Estimation 60F05: Central limit and other weak theorems

Keywords
Product-limit estimator truncated data censoring strong consistency weak convergence empirical process stochastic integral martingales

Citation

Lai, Tze Leung; Ying, Zhiliang. Estimating a Distribution Function with Truncated and Censored Data. Ann. Statist. 19 (1991), no. 1, 417--442. doi:10.1214/aos/1176347991. https://projecteuclid.org/euclid.aos/1176347991


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