A composite nonparametric product limit approach for estimating the distribution of survival times under length-biased and right-censored data

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

View graph of relations

Related Research Unit(s)


Original languageEnglish
Pages (from-to)221-235
Journal / PublicationStatistics and its Interface
Issue number2
Publication statusPublished - 2020


This paper considers a composite nonparametric product limit estimator for estimating the distribution of survival times when the data are length-biased and right censored. Our method takes into account auxiliary information that frequently arises in survival analysis, and is easier to implement than existing methods for estimating survival functions. We derive a strong representation of the proposed estimator, establish its consistency and asymptotic normality, and derive its convergence rate of approximation. As well, we prove that auxiliary information improves the asymptotic efficiency of the proposed estimator, and provide the values of the composite weights that result in the largest efficiency gain. Our proposed estimator fares well in comparison with other more complex methods in finite samples and offers a clear advantage with respect to computational time.

Research Area(s)

  • Almost sure representation, Biased data, censored, Composite nonparametric estimator, Product-limit estimator, Right, Strong consistency

Citation Format(s)