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December, 1986 Asymptotic Properties of the Product Limit Estimate Under Random Truncation
Mei-Cheng Wang, Nicholas P. Jewell, Wei-Yann Tsai
Ann. Statist. 14(4): 1597-1605 (December, 1986). DOI: 10.1214/aos/1176350180


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.


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Mei-Cheng Wang. Nicholas P. Jewell. Wei-Yann Tsai. "Asymptotic Properties of the Product Limit Estimate Under Random Truncation." Ann. Statist. 14 (4) 1597 - 1605, December, 1986.


Published: December, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0656.62048
MathSciNet: MR868322
Digital Object Identifier: 10.1214/aos/1176350180

Primary: 62G05

Rights: Copyright © 1986 Institute of Mathematical Statistics


Vol.14 • No. 4 • December, 1986
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