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VOL. 54 | 2007 Nonparametric estimation of a distribution function under biased sampling and censoring


This paper derives the nonparametric maximum likelihood estimator (NPMLE) of a distribution function from observations which are subject to both bias and censoring. The NPMLE is obtained by a simple EM algorithm which is an extension of the algorithm suggested by Vardi (Biometrika, 1989) for size biased data. Application of the algorithm to many models is discussed and a simulation study compares the estimator's performance to that of the product-limit estimator (PLE). An example demonstrates the utility of the NPMLE to data where the PLE is inappropriate.


Published: 1 January 2007
First available in Project Euclid: 4 December 2007

MathSciNet: MR2459191

Digital Object Identifier: 10.1214/074921707000000175

Primary: 62N01

Keywords: cross-sectional sampling , EM algorithm , Lexis diagram , Multiplicative censoring , truncated data

Rights: Copyright © 2007, Institute of Mathematical Statistics


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