The Annals of Statistics

A Large Sample Study of the Life Table and Product Limit Estimates Under Random Censorship

N. Breslow and J. Crowley

Full-text: Open access

Abstract

Using the model of random censorship, a necessary and sufficient condition for the consistency of the standard (actuarial) life table estimate of a survival distribution is derived. We establish the asymptotic normality of this estimate, showing that Greenwood's variance formula is nearly correct. In the case of a continuous survival distribution we establish limiting normality for the product limit estimate and for the closely related cumulative hazard process. Some applications of these results are outlined.

Article information

Source
Ann. Statist., Volume 2, Number 3 (1974), 437-453.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176342705

Digital Object Identifier
doi:10.1214/aos/1176342705

Mathematical Reviews number (MathSciNet)
MR458674

Zentralblatt MATH identifier
0283.62023

JSTOR
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62G05: Estimation

Keywords
Life table product limit censored data consistency weak convergence

Citation

Breslow, N.; Crowley, J. A Large Sample Study of the Life Table and Product Limit Estimates Under Random Censorship. Ann. Statist. 2 (1974), no. 3, 437--453. doi:10.1214/aos/1176342705. https://projecteuclid.org/euclid.aos/1176342705


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