The Annals of Statistics
- Ann. Statist.
- Volume 19, Number 1 (1991), 417-442.
Estimating a Distribution Function with Truncated and Censored Data
A minor modification of the product-limit estimator is proposed for estimating a distribution function (not necessarily continuous) when the data are subject to either truncation or censoring, or to both, by independent but not necessarily identically distributed truncation-censoring variables. Making use of martingale integral representations and empirical process theory, uniform strong consistency of the estimator is established and weak convergence results are proved for the entire observable range of the function. Numerical results are also given to illustrate the usefulness of the modification, particularly in the context of truncated data.
Ann. Statist., Volume 19, Number 1 (1991), 417-442.
First available in Project Euclid: 12 April 2007
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Lai, Tze Leung; Ying, Zhiliang. Estimating a Distribution Function with Truncated and Censored Data. Ann. Statist. 19 (1991), no. 1, 417--442. doi:10.1214/aos/1176347991. https://projecteuclid.org/euclid.aos/1176347991