Institute of Mathematical Statistics Lecture Notes - Monograph Series

Nonparametric estimation of a distribution function under biased sampling and censoring

Micha Mandel

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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.

Chapter information

Regina Liu, William Strawderman and Cun-Hui Zhang, eds., Complex Datasets and Inverse Problems: Tomography, Networks and Beyond (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2007), 224-238

First available in Project Euclid: 4 December 2007

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Mathematical Reviews number (MathSciNet)

Primary: 62N01: Censored data models

cross-sectional sampling EM algorithm Lexis diagram multiplicative censoring truncated data

Copyright © 2007, Institute of Mathematical Statistics


Mandel, Micha. Nonparametric estimation of a distribution function under biased sampling and censoring. Complex Datasets and Inverse Problems, 224--238, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2007. doi:10.1214/074921707000000175.

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