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)...

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Bibliographic Details
Published inLecture notes-monograph series Vol. 54; pp. 224 - 238
Main Author Mandel, Micha
Format Journal Article
LanguageEnglish
Published Institute of Mathematical Statistics 01.01.2007
Subjects
Age
Censored data
Censorship
Datasets
Distribution functions
Estimation bias
Estimators
Poisson process
Sampling bias
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Summary: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.
ISSN:0749-2170
DOI:10.1214/074921707000000175