Institute of Mathematical Statistics Lecture Notes - Monograph Series

Sieve estimates for biased survival data

Jiayang Sun and Bin Wang

Full-text: Open access


In studies involving lifetimes, observed survival times are frequently censored and possibly subject to biased sampling. In this paper, we model survival times under biased sampling (a.k.a., biased survival data) by a semi-parametric model, in which the selection function $w(t)$ (that leads to the biased sampling) is specified up to an unknown finite dimensional parameter $\theta$, while the density function $f(t)$ of the survival times is assumed only to be smooth. Under this model, two estimators are derived to estimate the density function $f$, and a pseudo maximum likelihood estimation procedure is developed to estimate $\theta$. The identifiability of the estimation problem is discussed and the performance of the new estimators is illustrated via both simulation studies and a real data application.

Chapter information

Jiayang Sun, Anirban DasGupta, Vince Melfi, Connie Page, eds., Recent Developments in Nonparametric Inference and Probability: Festschrift for Michael Woodroofe (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 127-143

First available: 28 November 2007

Permanent link to this document

Digital Object Identifier

Primary: S62N01 62D05: Sampling theory, sample surveys
Secondary: 62G07: Density estimation

semi-parametric model biased sampling weighted kernel estimate transformation-based estimate cross-validation non-ignorable missing


Sun, Jiayang; Wang, Bin. Sieve estimates for biased survival data. Recent Developments in Nonparametric Inference and Probability, 127--143, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000644.

Export citation