The Annals of Statistics

Asymptotic Properties of the Product Limit Estimate Under Random Truncation

Mei-Cheng Wang, Nicholas P. Jewell, and Wei-Yann Tsai

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Abstract

Many authors have considered the problem of estimating a distribution function when the observed data is subject to random truncation. A prominent role is played by the product limit estimator, which is the analogue of the Kaplan-Meier estimator of a distribution function under random censoring. Wang and Jewell (1985) and Woodroofe (1985) independently proved consistency results for this product limit estimator and showed weak convergence to a Gaussian process. Both papers left open the exact form of the covariance structure of the limiting process. Here we provide a precise description of the asymptotic behavior of the product limit estimator, including a simple explicit form of the asymptotic covariance structure, which also turns out to be the analogue of the covariance structure of the Kaplan-Meier estimator. Some applications are briefly discussed.

Article information

Source
Ann. Statist. Volume 14, Number 4 (1986), 1597-1605.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176350180

Digital Object Identifier
doi:10.1214/aos/1176350180

Mathematical Reviews number (MathSciNet)
MR868322

Zentralblatt MATH identifier
0656.62048

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation

Keywords
Product limit truncated data weak convergence covariance structure

Citation

Wang, Mei-Cheng; Jewell, Nicholas P.; Tsai, Wei-Yann. Asymptotic Properties of the Product Limit Estimate Under Random Truncation. Ann. Statist. 14 (1986), no. 4, 1597--1605. doi:10.1214/aos/1176350180. http://projecteuclid.org/euclid.aos/1176350180.


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