Nonparametric estimation of a distribution function under biased sampling and censoring

TL;DR

This paper develops a nonparametric maximum likelihood estimator for distribution functions from biased and censored data, using an EM algorithm, and compares its performance to traditional methods through simulations and examples.

Contribution

It introduces a simple EM algorithm to compute the NPMLE for biased and censored data, extending previous algorithms for size-biased data.

Findings

The NPMLE performs better than the product-limit estimator in biased and censored scenarios.

Simulation results show the estimator's robustness across various models.

An example illustrates the estimator's practical utility where PLE is inadequate.

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.