Annals of Statistics

A Large Sample Study of Generalized Maximum Likelihood Estimators from Incomplete Data Via Self-Consistency

Wei-Yann Tsai and John Crowley

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Abstract

Self-consistent estimators for estimating distribution functions from incomplete data are presented. In many cases these estimators are also generalized maximum likelihood estimators. In this paper we discuss the theoretical properties of such estimators: existence, uniform consistency, law of the iterated logarithm, and weak convergence. Applications to the product limit estimator for right-censored data and to the estimator proposed by Turnbull (1974, 1976) for doubly (right- and left-) censored data are also given.

Article information

Source
Ann. Statist., Volume 13, Number 4 (1985), 1317-1334.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349740

Digital Object Identifier
doi:10.1214/aos/1176349740

Mathematical Reviews number (MathSciNet)
MR811495

Zentralblatt MATH identifier
0611.62038

JSTOR
links.jstor.org

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

Keywords
Generalized maximum likelihood estimator self-consistency incomplete data implicit function theorem uniform consistency law of the iterated logarithm weak convergence product limit estimator censored data

Citation

Tsai, Wei-Yann; Crowley, John. A Large Sample Study of Generalized Maximum Likelihood Estimators from Incomplete Data Via Self-Consistency. Ann. Statist. 13 (1985), no. 4, 1317--1334. doi:10.1214/aos/1176349740. https://projecteuclid.org/euclid.aos/1176349740


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Corrections

  • See Correction: Wei-Yann Tsai, John Crowley. Correction: A Large Sample Study of Generalized Maximum Likelihood Estimators from Incomplete Data via Self-Consistency. Ann. Statist., Volume 18, Number 1 (1990), 470--470.