Open Access
June, 1982 Asymptotic Optimality of the Product Limit Estimator
Jon A. Wellner
Ann. Statist. 10(2): 595-602 (June, 1982). DOI: 10.1214/aos/1176345800


The product limit estimator due to Kaplan and Meier (1958) is well-known to be the nonparametric maximum likelihood estimator of a distribution function based on censored data. It is shown here that the product limit estimator is an asymptotically optimal estimator in two senses: in the sense of a Hajek-Beran type representation theorem for regular estimators; and in an asymptotic minimax sense similar to the classical result for the uncensored case due to Dvoretzky, Kiefer, and Wolfowitz (1956). The proofs rely on the methods of Beran (1977) and Millar (1979).


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Jon A. Wellner. "Asymptotic Optimality of the Product Limit Estimator." Ann. Statist. 10 (2) 595 - 602, June, 1982.


Published: June, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0489.62036
MathSciNet: MR653534
Digital Object Identifier: 10.1214/aos/1176345800

Primary: 62G05
Secondary: 62E20 , 62G20

Keywords: asymptotic minimax , Censored data , convolution representation , distribution function , regular estimation

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 2 • June, 1982
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