The Annals of Statistics
- Ann. Statist.
- Volume 14, Number 4 (1986), 1597-1605.
Asymptotic Properties of the Product Limit Estimate Under Random Truncation
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.
Ann. Statist. Volume 14, Number 4 (1986), 1597-1605.
First available in Project Euclid: 12 April 2007
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62G05: Estimation
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. https://projecteuclid.org/euclid.aos/1176350180.