The Annals of Statistics

Large Sample Behaviour of the Product-Limit Estimator on the Whole Line

Richard Gill

Full-text: Open access

Abstract

Weak convergence results are proved for the product-limit estimator on the whole line. Applications are given to confidence band construction, estimation of mean lifetime, and to the theory of $q$-functions. The results are obtained using stochastic calculus and in probability linear bounds for empirical processes.

Article information

Source
Ann. Statist., Volume 11, Number 1 (1983), 49-58.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346055

Digital Object Identifier
doi:10.1214/aos/1176346055

Mathematical Reviews number (MathSciNet)
MR684862

Zentralblatt MATH identifier
0518.62039

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62G15: Tolerance and confidence regions 60F05: Central limit and other weak theorems 62N05: Reliability and life testing [See also 90B25] 62P10: Applications to biology and medical sciences

Keywords
Product-limit estimator Kaplan-Meier estimator random censorship survival data confidence bands mean life-time counting processes martingales stochastic integrals weak convergence in probability linear bounds $q$-functions censored data

Citation

Gill, Richard. Large Sample Behaviour of the Product-Limit Estimator on the Whole Line. Ann. Statist. 11 (1983), no. 1, 49--58. doi:10.1214/aos/1176346055. https://projecteuclid.org/euclid.aos/1176346055


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