Institute of Mathematical Statistics Lecture Notes - Monograph Series

Sieve estimates for biased survival data

Jiayang Sun and Bin Wang

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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 in Project Euclid: 28 November 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH 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

Copyright © 2006, Institute of Mathematical Statistics


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.

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