作者
Mei-Cheng Wang, Nicholas P Jewell, Wei-Yann Tsai
发表日期
1986/12/1
期刊
the Annals of Statistics
页码范围
1597-1605
出版商
Institute of Mathematical Statistics
简介
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.
引用总数
学术搜索中的文章
MC Wang, NP Jewell, WY Tsai - the Annals of Statistics, 1986