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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Abstract

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

Source
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

Dates
First available in Project Euclid: 4 December 2007

Permanent link to this document
https://projecteuclid.org/euclid.lnms/1196794955

Digital Object Identifier
doi:10.1214/074921707000000175

Mathematical Reviews number (MathSciNet)
MR2459191

Subjects
Primary: 62N01: Censored data models

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

Rights
Copyright © 2007, Institute of Mathematical Statistics

Citation

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. https://projecteuclid.org/euclid.lnms/1196794955


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